LMFDB - Embedded newform 210.3.k.a.167.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(83,210)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("210.83");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			167.4
Character	$\chi$	$=$	210.167
Dual form			210.3.k.a.83.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-2.28799 + 1.94039i) q^{3} -2.00000i q^{4} +(4.58449 + 1.99562i) q^{5} +(0.347606 - 4.22838i) q^{6} +(5.57668 - 4.23091i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.46981 - 8.87917i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-2.28799 + 1.94039i) q^{3} -2.00000i q^{4} +(4.58449 + 1.99562i) q^{5} +(0.347606 - 4.22838i) q^{6} +(5.57668 - 4.23091i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.46981 - 8.87917i) q^{9} +(-6.58010 + 2.58887i) q^{10} -14.6047i q^{11} +(3.88077 + 4.57598i) q^{12} +(-3.48167 - 3.48167i) q^{13} +(-1.34578 + 9.80759i) q^{14} +(-14.3615 + 4.32971i) q^{15} -4.00000 q^{16} +(20.1653 + 20.1653i) q^{17} +(7.40936 + 10.3490i) q^{18} +26.4132 q^{19} +(3.99123 - 9.16897i) q^{20} +(-4.54981 + 20.5012i) q^{21} +(14.6047 + 14.6047i) q^{22} +(-2.68095 - 2.68095i) q^{23} +(-8.45675 - 0.695213i) q^{24} +(17.0350 + 18.2978i) q^{25} +6.96334 q^{26} +(13.8661 + 23.1675i) q^{27} +(-8.46182 - 11.1534i) q^{28} -28.5159 q^{29} +(10.0318 - 18.6912i) q^{30} +15.6511i q^{31} +(4.00000 - 4.00000i) q^{32} +(28.3387 + 33.4154i) q^{33} -40.3306 q^{34} +(34.0095 - 8.26762i) q^{35} +(-17.7583 - 2.93962i) q^{36} +(7.69844 + 7.69844i) q^{37} +(-26.4132 + 26.4132i) q^{38} +(14.7218 + 1.21025i) q^{39} +(5.17774 + 13.1602i) q^{40} -37.9832 q^{41} +(-15.9514 - 25.0510i) q^{42} +(41.7817 - 41.7817i) q^{43} -29.2094 q^{44} +(24.4578 - 37.7732i) q^{45} +5.36190 q^{46} +(-21.0822 - 21.0822i) q^{47} +(9.15197 - 7.76154i) q^{48} +(13.1988 - 47.1889i) q^{49} +(-35.3328 - 1.26273i) q^{50} +(-85.2664 - 7.00958i) q^{51} +(-6.96334 + 6.96334i) q^{52} +(47.4934 + 47.4934i) q^{53} +(-37.0336 - 9.30137i) q^{54} +(29.1453 - 66.9549i) q^{55} +(19.6152 + 2.69155i) q^{56} +(-60.4332 + 51.2518i) q^{57} +(28.5159 - 28.5159i) q^{58} -61.6589i q^{59} +(8.65943 + 28.7231i) q^{60} +54.1777i q^{61} +(-15.6511 - 15.6511i) q^{62} +(-29.3703 - 55.7350i) q^{63} +8.00000i q^{64} +(-9.01359 - 22.9098i) q^{65} +(-61.7541 - 5.07668i) q^{66} +(68.9882 + 68.9882i) q^{67} +(40.3306 - 40.3306i) q^{68} +(11.3361 + 0.931915i) q^{69} +(-25.7419 + 42.2771i) q^{70} -65.9594i q^{71} +(20.6980 - 14.8187i) q^{72} +(6.51081 + 6.51081i) q^{73} -15.3969 q^{74} +(-74.4807 - 8.81061i) q^{75} -52.8265i q^{76} +(-61.7911 - 81.4457i) q^{77} +(-15.9321 + 13.5116i) q^{78} -42.7301i q^{79} +(-18.3379 - 7.98247i) q^{80} +(-76.6793 - 26.1014i) q^{81} +(37.9832 - 37.9832i) q^{82} +(-9.52614 + 9.52614i) q^{83} +(41.0024 + 9.09963i) q^{84} +(52.2053 + 132.690i) q^{85} +83.5634i q^{86} +(65.2441 - 55.3318i) q^{87} +(29.2094 - 29.2094i) q^{88} +19.3830i q^{89} +(13.3155 + 62.2310i) q^{90} +(-34.1468 - 4.68555i) q^{91} +(-5.36190 + 5.36190i) q^{92} +(-30.3692 - 35.8096i) q^{93} +42.1644 q^{94} +(121.091 + 52.7107i) q^{95} +(-1.39043 + 16.9135i) q^{96} +(-84.6391 + 84.6391i) q^{97} +(33.9901 + 60.3877i) q^{98} +(-129.677 - 21.4661i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} - 4 q^{7} + 64 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q - 32 * q^2 - 4 * q^7 + 64 * q^8 - 16 * q^9	$ 32 q - 32 q^{2} - 4 q^{7} + 64 q^{8} - 16 q^{9} + 8 q^{14} - 20 q^{15} - 128 q^{16} + 36 q^{18} + 12 q^{21} - 40 q^{22} + 24 q^{23} + 16 q^{25} - 8 q^{28} - 112 q^{29} + 68 q^{30} + 128 q^{32} - 48 q^{35} - 40 q^{36} + 32 q^{37} + 64 q^{39} - 44 q^{42} - 32 q^{43} + 80 q^{44} - 48 q^{46} - 8 q^{50} + 84 q^{51} - 136 q^{53} + 244 q^{57} + 112 q^{58} - 96 q^{60} + 72 q^{63} - 200 q^{65} + 32 q^{67} + 8 q^{72} - 64 q^{74} + 88 q^{77} - 124 q^{78} + 76 q^{81} + 64 q^{84} - 40 q^{85} - 80 q^{88} - 272 q^{91} + 48 q^{92} - 452 q^{93} + 544 q^{95} + 128 q^{98} + 160 q^{99}+O(q^{100}) $ 32 * q - 32 * q^2 - 4 * q^7 + 64 * q^8 - 16 * q^9 + 8 * q^14 - 20 * q^15 - 128 * q^16 + 36 * q^18 + 12 * q^21 - 40 * q^22 + 24 * q^23 + 16 * q^25 - 8 * q^28 - 112 * q^29 + 68 * q^30 + 128 * q^32 - 48 * q^35 - 40 * q^36 + 32 * q^37 + 64 * q^39 - 44 * q^42 - 32 * q^43 + 80 * q^44 - 48 * q^46 - 8 * q^50 + 84 * q^51 - 136 * q^53 + 244 * q^57 + 112 * q^58 - 96 * q^60 + 72 * q^63 - 200 * q^65 + 32 * q^67 + 8 * q^72 - 64 * q^74 + 88 * q^77 - 124 * q^78 + 76 * q^81 + 64 * q^84 - 40 * q^85 - 80 * q^88 - 272 * q^91 + 48 * q^92 - 452 * q^93 + 544 * q^95 + 128 * q^98 + 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	−2.28799	+	1.94039i	−0.762664	+	0.646795i
$3$	−2.28799	+	1.94039i	−0.762664	+	0.646795i
$4$		−	2.00000i		−	0.500000i
$5$	4.58449	+	1.99562i	0.916897	+	0.399123i
$5$	4.58449	+	1.99562i	0.916897	+	0.399123i
$6$	0.347606	−	4.22838i	0.0579344	−	0.704729i
$7$	5.57668	−	4.23091i	0.796669	−	0.604416i
$7$	5.57668	−	4.23091i	0.796669	−	0.604416i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	1.46981	−	8.87917i	0.163312	−	0.986574i
$10$	−6.58010	+	2.58887i	−0.658010	+	0.258887i
$11$		−	14.6047i		−	1.32770i	−0.747867	−	0.663849i	$-0.768922\pi$
$11$		−	14.6047i		−	1.32770i	0.747867	−	0.663849i	$-0.231078\pi$
$12$	3.88077	+	4.57598i	0.323398	+	0.381332i
$13$	−3.48167	−	3.48167i	−0.267821	−	0.267821i	0.560401	−	0.828222i	$-0.310647\pi$
$13$	−3.48167	−	3.48167i	−0.267821	−	0.267821i	−0.828222	+	0.560401i	$0.810647\pi$
$14$	−1.34578	+	9.80759i	−0.0961268	+	0.700542i
$15$	−14.3615	+	4.32971i	−0.957435	+	0.288648i
$16$	−4.00000			−0.250000
$17$	20.1653	+	20.1653i	1.18619	+	1.18619i	0.978112	+	0.208081i	$0.0667219\pi$
$17$	20.1653	+	20.1653i	1.18619	+	1.18619i	0.208081	+	0.978112i	$0.433278\pi$
$18$	7.40936	+	10.3490i	0.411631	+	0.574943i
$19$	26.4132			1.39017			0.695085	−	0.718928i	$-0.255367\pi$
$19$	26.4132			1.39017			0.695085	+	0.718928i	$0.255367\pi$
$20$	3.99123	−	9.16897i	0.199562	−	0.458449i
$21$	−4.54981	+	20.5012i	−0.216658	+	0.976248i
$22$	14.6047	+	14.6047i	0.663849	+	0.663849i
$23$	−2.68095	−	2.68095i	−0.116563	−	0.116563i	0.646419	−	0.762982i	$-0.276266\pi$
$23$	−2.68095	−	2.68095i	−0.116563	−	0.116563i	−0.762982	+	0.646419i	$0.776266\pi$
$24$	−8.45675	−	0.695213i	−0.352365	−	0.0289672i
$25$	17.0350	+	18.2978i	0.681401	+	0.731910i
$26$	6.96334			0.267821
$27$	13.8661	+	23.1675i	0.513559	+	0.858054i
$28$	−8.46182	−	11.1534i	−0.302208	−	0.398335i
$29$	−28.5159			−0.983306			−0.491653	−	0.870791i	$-0.663607\pi$
$29$	−28.5159			−0.983306			−0.491653	+	0.870791i	$0.663607\pi$
$30$	10.0318	−	18.6912i	0.334394	−	0.623041i
$31$			15.6511i			0.504875i	0.967613	+	0.252438i	$0.0812322\pi$
$31$			15.6511i			0.504875i	−0.967613	+	0.252438i	$0.918768\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	28.3387	+	33.4154i	0.858748	+	1.01259i
$34$	−40.3306			−1.18619
$35$	34.0095	−	8.26762i	0.971700	−	0.236218i
$36$	−17.7583	−	2.93962i	−0.493287	−	0.0816562i
$37$	7.69844	+	7.69844i	0.208066	+	0.208066i	0.803445	−	0.595379i	$-0.202998\pi$
$37$	7.69844	+	7.69844i	0.208066	+	0.208066i	−0.595379	+	0.803445i	$0.702998\pi$
$38$	−26.4132	+	26.4132i	−0.695085	+	0.695085i
$39$	14.7218	+	1.21025i	0.377483	+	0.0310321i
$40$	5.17774	+	13.1602i	0.129443	+	0.329005i
$41$	−37.9832			−0.926419			−0.463209	−	0.886249i	$-0.653302\pi$
$41$	−37.9832			−0.926419			−0.463209	+	0.886249i	$0.653302\pi$
$42$	−15.9514	−	25.0510i	−0.379795	−	0.596453i
$43$	41.7817	−	41.7817i	0.971667	−	0.971667i	−0.0279426	−	0.999610i	$-0.508896\pi$
$43$	41.7817	−	41.7817i	0.971667	−	0.971667i	0.999610	+	0.0279426i	$0.00889555\pi$
$44$	−29.2094			−0.663849
$45$	24.4578	−	37.7732i	0.543506	−	0.839406i
$46$	5.36190			0.116563
$47$	−21.0822	−	21.0822i	−0.448558	−	0.448558i	0.446317	−	0.894875i	$-0.352735\pi$
$47$	−21.0822	−	21.0822i	−0.448558	−	0.448558i	−0.894875	+	0.446317i	$0.852735\pi$
$48$	9.15197	−	7.76154i	0.190666	−	0.161699i
$49$	13.1988	−	47.1889i	0.269364	−	0.963039i
$50$	−35.3328	−	1.26273i	−0.706656	−	0.0252547i
$51$	−85.2664	−	7.00958i	−1.67189	−	0.137443i
$52$	−6.96334	+	6.96334i	−0.133910	+	0.133910i
$53$	47.4934	+	47.4934i	0.896102	+	0.896102i	0.995089	−	0.0989866i	$-0.0315601\pi$
$53$	47.4934	+	47.4934i	0.896102	+	0.896102i	−0.0989866	+	0.995089i	$0.531560\pi$
$54$	−37.0336	−	9.30137i	−0.685807	−	0.172248i
$55$	29.1453	−	66.9549i	0.529915	−	1.21736i
$56$	19.6152	+	2.69155i	0.350271	+	0.0480634i
$57$	−60.4332	+	51.2518i	−1.06023	+	0.899155i
$58$	28.5159	−	28.5159i	0.491653	−	0.491653i
$59$		−	61.6589i		−	1.04507i	−0.852619	−	0.522533i	$-0.824987\pi$
$59$		−	61.6589i		−	1.04507i	0.852619	−	0.522533i	$-0.175013\pi$
$60$	8.65943	+	28.7231i	0.144324	+	0.478718i
$61$			54.1777i			0.888159i	0.895987	+	0.444080i	$0.146469\pi$
$61$			54.1777i			0.888159i	−0.895987	+	0.444080i	$0.853531\pi$
$62$	−15.6511	−	15.6511i	−0.252438	−	0.252438i
$63$	−29.3703	−	55.7350i	−0.466195	−	0.884682i
$64$			8.00000i			0.125000i
$65$	−9.01359	−	22.9098i	−0.138671	−	0.352458i
$66$	−61.7541	−	5.07668i	−0.935668	−	0.0769194i
$67$	68.9882	+	68.9882i	1.02967	+	1.02967i	0.999546	+	0.0301280i	$0.00959148\pi$
$67$	68.9882	+	68.9882i	1.02967	+	1.02967i	0.0301280	+	0.999546i	$0.490409\pi$
$68$	40.3306	−	40.3306i	0.593096	−	0.593096i
$69$	11.3361	+	0.931915i	0.164291	+	0.0135060i
$70$	−25.7419	+	42.2771i	−0.367741	+	0.603959i
$71$		−	65.9594i		−	0.929006i	−0.885572	−	0.464503i	$-0.846233\pi$
$71$		−	65.9594i		−	0.929006i	0.885572	−	0.464503i	$-0.153767\pi$
$72$	20.6980	−	14.8187i	0.287472	−	0.205816i
$73$	6.51081	+	6.51081i	0.0891892	+	0.0891892i	0.750294	−	0.661105i	$-0.229912\pi$
$73$	6.51081	+	6.51081i	0.0891892	+	0.0891892i	−0.661105	+	0.750294i	$0.729912\pi$
$74$	−15.3969			−0.208066
$75$	−74.4807	−	8.81061i	−0.993076	−	0.117475i
$76$		−	52.8265i		−	0.695085i
$77$	−61.7911	−	81.4457i	−0.802481	−	1.05774i
$78$	−15.9321	+	13.5116i	−0.204257	+	0.173225i
$79$		−	42.7301i		−	0.540887i	−0.962736	−	0.270443i	$-0.912830\pi$
$79$		−	42.7301i		−	0.540887i	0.962736	−	0.270443i	$-0.0871703\pi$
$80$	−18.3379	−	7.98247i	−0.229224	−	0.0997809i
$81$	−76.6793	−	26.1014i	−0.946658	−	0.322240i
$82$	37.9832	−	37.9832i	0.463209	−	0.463209i
$83$	−9.52614	+	9.52614i	−0.114773	+	0.114773i	−0.762161	−	0.647388i	$-0.775861\pi$
$83$	−9.52614	+	9.52614i	−0.114773	+	0.114773i	0.647388	+	0.762161i	$0.275861\pi$
$84$	41.0024	+	9.09963i	0.488124	+	0.108329i
$85$	52.2053	+	132.690i	0.614180	+	1.56105i
$86$			83.5634i			0.971667i
$87$	65.2441	−	55.3318i	0.749932	−	0.635998i
$88$	29.2094	−	29.2094i	0.331924	−	0.331924i
$89$			19.3830i			0.217786i	0.994053	+	0.108893i	$0.0347306\pi$
$89$			19.3830i			0.217786i	−0.994053	+	0.108893i	$0.965269\pi$
$90$	13.3155	+	62.2310i	0.147950	+	0.691456i
$91$	−34.1468	−	4.68555i	−0.375240	−	0.0514895i
$92$	−5.36190	+	5.36190i	−0.0582815	+	0.0582815i
$93$	−30.3692	−	35.8096i	−0.326551	−	0.385050i
$94$	42.1644			0.448558
$95$	121.091	+	52.7107i	1.27464	+	0.554849i
$96$	−1.39043	+	16.9135i	−0.0144836	+	0.176182i
$97$	−84.6391	+	84.6391i	−0.872568	+	0.872568i	−0.992752	−	0.120184i	$-0.961652\pi$
$97$	−84.6391	+	84.6391i	−0.872568	+	0.872568i	0.120184	+	0.992752i	$0.461652\pi$
$98$	33.9901	+	60.3877i	0.346837	+	0.616201i
$99$	−129.677	−	21.4661i	−1.30987	−	0.216829i
$100$	36.5955	−	34.0700i	0.365955	−	0.340700i
$101$	112.859			1.11741			0.558707	−	0.829365i	$-0.311298\pi$
$101$	112.859			1.11741			0.558707	+	0.829365i	$0.311298\pi$
$102$	92.2760	−	78.2568i	0.904666	−	0.767224i
$103$	−82.5883	−	82.5883i	−0.801828	−	0.801828i	0.181553	−	0.983381i	$-0.441888\pi$
$103$	−82.5883	−	82.5883i	−0.801828	−	0.801828i	−0.983381	+	0.181553i	$0.941888\pi$
$104$		−	13.9267i		−	0.133910i
$105$	−61.7711	+	84.9078i	−0.588296	+	0.808646i
$106$	−94.9868			−0.896102
$107$	−125.554	+	125.554i	−1.17340	+	1.17340i	−0.192011	+	0.981393i	$0.561501\pi$
$107$	−125.554	+	125.554i	−1.17340	+	1.17340i	−0.981393	+	0.192011i	$0.938499\pi$
$108$	46.3349	−	27.7322i	0.429027	−	0.256780i
$109$			1.60754i			0.0147481i	0.999973	+	0.00737405i	$0.00234725\pi$
$109$			1.60754i			0.0147481i	−0.999973	+	0.00737405i	$0.997653\pi$
$110$	37.8096	+	96.1003i	0.343724	+	0.873639i
$111$	−32.5519	−	2.67603i	−0.293261	−	0.0241084i
$112$	−22.3067	+	16.9236i	−0.199167	+	0.151104i
$113$	−141.505	−	141.505i	−1.25226	−	1.25226i	−0.954704	−	0.297556i	$-0.903828\pi$
$113$	−141.505	−	141.505i	−1.25226	−	1.25226i	−0.297556	−	0.954704i	$-0.596172\pi$
$114$	9.18141	−	111.685i	0.0805387	−	0.979694i
$115$	−6.94062	−	17.6409i	−0.0603532	−	0.153399i
$116$			57.0318i			0.491653i
$117$	−36.0318	+	25.7970i	−0.307964	+	0.220487i
$118$	61.6589	+	61.6589i	0.522533	+	0.522533i
$119$	197.773	+	27.1379i	1.66196	+	0.228050i
$120$	−37.3825	−	20.0636i	−0.311521	−	0.167197i
$121$	−92.2966			−0.762782
$122$	−54.1777	−	54.1777i	−0.444080	−	0.444080i
$123$	86.9052	−	73.7020i	0.706546	−	0.599203i
$124$	31.3023			0.252438
$125$	41.5815	+	117.881i	0.332652	+	0.943050i
$126$	85.1053	+	26.3647i	0.675439	+	0.209243i
$127$	−39.5166	−	39.5166i	−0.311154	−	0.311154i	0.534202	−	0.845357i	$-0.320612\pi$
$127$	−39.5166	−	39.5166i	−0.311154	−	0.311154i	−0.845357	+	0.534202i	$0.820612\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$	−14.5236	+	176.669i	−0.112586	+	1.36952i
$130$	31.9234	+	13.8962i	0.245564	+	0.106894i
$131$	122.046			0.931652			0.465826	−	0.884876i	$-0.345757\pi$
$131$	122.046			0.931652			0.465826	+	0.884876i	$0.345757\pi$
$132$	66.8308	−	56.6774i	0.506294	−	0.429374i
$133$	147.298	−	111.752i	1.10751	−	0.840240i
$134$	−137.976			−1.02967
$135$	17.3355	+	133.882i	0.128411	+	0.991721i
$136$			80.6611i			0.593096i
$137$	141.949	−	141.949i	1.03612	−	1.03612i	0.0368001	−	0.999323i	$-0.488284\pi$
$137$	141.949	−	141.949i	1.03612	−	1.03612i	0.999323	−	0.0368001i	$-0.0117165\pi$
$138$	−12.2680	+	10.4041i	−0.0888984	+	0.0753924i
$139$	41.4554			0.298240			0.149120	−	0.988819i	$-0.452356\pi$
$139$	41.4554			0.298240			0.149120	+	0.988819i	$0.452356\pi$
$140$	−16.5352	−	68.0190i	−0.118109	−	0.485850i
$141$	89.1435	+	7.32831i	0.632224	+	0.0519739i
$142$	65.9594	+	65.9594i	0.464503	+	0.464503i
$143$	−50.8487	+	50.8487i	−0.355585	+	0.355585i
$144$	−5.87924	+	35.5167i	−0.0408281	+	0.246644i
$145$	−130.731	−	56.9068i	−0.901591	−	0.392461i
$146$	−13.0216			−0.0891892
$147$	61.3658	+	133.579i	0.417455	+	0.908698i
$148$	15.3969	−	15.3969i	0.104033	−	0.104033i
$149$	189.375			1.27097			0.635485	−	0.772113i	$-0.280800\pi$
$149$	189.375			1.27097			0.635485	+	0.772113i	$0.280800\pi$
$150$	83.2913	−	65.6701i	0.555275	−	0.437801i
$151$	−117.328			−0.777007			−0.388503	−	0.921447i	$-0.627008\pi$
$151$	−117.328			−0.777007			−0.388503	+	0.921447i	$0.627008\pi$
$152$	52.8265	+	52.8265i	0.347542	+	0.347542i
$153$	208.690	−	149.412i	1.36399	−	0.976548i
$154$	143.237	+	19.6546i	0.930109	+	0.127627i
$155$	−31.2337	+	71.7524i	−0.201507	+	0.462919i
$156$	2.42050	−	29.4436i	0.0155160	−	0.188741i
$157$	−123.504	+	123.504i	−0.786651	+	0.786651i	−0.980944	−	0.194293i	$-0.937759\pi$
$157$	−123.504	+	123.504i	−0.786651	+	0.786651i	0.194293	+	0.980944i	$0.437759\pi$
$158$	42.7301	+	42.7301i	0.270443	+	0.270443i
$159$	−200.820	−	16.5090i	−1.26302	−	0.103830i
$160$	26.3204	−	10.3555i	0.164503	−	0.0647217i
$161$	−26.2937	−	3.60795i	−0.163315	−	0.0224096i
$162$	102.781	−	50.5779i	0.634449	−	0.312209i
$163$	−173.541	+	173.541i	−1.06467	+	1.06467i	−0.0669121	+	0.997759i	$0.521315\pi$
$163$	−173.541	+	173.541i	−1.06467	+	1.06467i	−0.997759	+	0.0669121i	$0.978685\pi$
$164$			75.9663i			0.463209i
$165$	63.2341	+	209.746i	0.383237	+	1.27119i
$166$		−	19.0523i		−	0.114773i
$167$	32.6021	+	32.6021i	0.195222	+	0.195222i	0.797948	−	0.602726i	$-0.205919\pi$
$167$	32.6021	+	32.6021i	0.195222	+	0.195222i	−0.602726	+	0.797948i	$0.705919\pi$
$168$	−50.1020	+	31.9028i	−0.298226	+	0.189897i
$169$		−	144.756i		−	0.856544i
$170$	−184.895	−	80.4844i	−1.08762	−	0.473437i
$171$	38.8225	−	234.528i	0.227032	−	1.37151i
$172$	−83.5634	−	83.5634i	−0.485833	−	0.485833i
$173$	−122.097	+	122.097i	−0.705761	+	0.705761i	−0.965641	−	0.259880i	$-0.916317\pi$
$173$	−122.097	+	122.097i	−0.705761	+	0.705761i	0.259880	+	0.965641i	$0.416317\pi$
$174$	−9.91231	+	120.576i	−0.0569673	+	0.692965i
$175$	172.415	+	29.9672i	0.985229	+	0.171241i
$176$			58.4187i			0.331924i
$177$	119.642	+	141.075i	0.675943	+	0.797034i
$178$	−19.3830	−	19.3830i	−0.108893	−	0.108893i
$179$	−48.8414			−0.272857			−0.136429	−	0.990650i	$-0.543562\pi$
$179$	−48.8414			−0.272857			−0.136429	+	0.990650i	$0.543562\pi$
$180$	−75.5465	−	48.9155i	−0.419703	−	0.271753i
$181$			74.5578i			0.411921i	0.978560	+	0.205961i	$0.0660319\pi$
$181$			74.5578i			0.411921i	−0.978560	+	0.205961i	$0.933968\pi$
$182$	38.8324	−	29.4613i	0.213365	−	0.161875i
$183$	−105.126	−	123.958i	−0.574457	−	0.677367i
$184$		−	10.7238i		−	0.0582815i
$185$	19.9303	+	50.6565i	0.107731	+	0.273819i
$186$	66.1789	+	5.44043i	0.355800	+	0.0292496i
$187$	294.507	−	294.507i	1.57491	−	1.57491i
$188$	−42.1644	+	42.1644i	−0.224279	+	0.224279i
$189$	175.346	+	70.5315i	0.927758	+	0.373182i
$190$	−173.802	+	68.3804i	−0.914746	+	0.359897i
$191$		−	22.0006i		−	0.115187i	−0.998340	−	0.0575933i	$-0.981657\pi$
$191$		−	22.0006i		−	0.115187i	0.998340	−	0.0575933i	$-0.0183427\pi$
$192$	−15.5231	−	18.3039i	−0.0808494	−	0.0953330i
$193$	−73.7660	+	73.7660i	−0.382207	+	0.382207i	−0.871897	−	0.489690i	$-0.837110\pi$
$193$	−73.7660	+	73.7660i	−0.382207	+	0.382207i	0.489690	+	0.871897i	$0.337110\pi$
$194$		−	169.278i		−	0.872568i
$195$	65.0768	+	34.9275i	0.333727	+	0.179115i
$196$	−94.3778	−	26.3976i	−0.481519	−	0.134682i
$197$	−124.480	+	124.480i	−0.631878	+	0.631878i	−0.948539	−	0.316661i	$-0.897438\pi$
$197$	−124.480	+	124.480i	−0.631878	+	0.631878i	0.316661	+	0.948539i	$0.397438\pi$
$198$	151.144	−	108.211i	0.763351	−	0.546522i
$199$	−324.188			−1.62908			−0.814542	−	0.580104i	$-0.803012\pi$
$199$	−324.188			−1.62908			−0.814542	+	0.580104i	$0.803012\pi$
$200$	−2.52547	+	70.6656i	−0.0126273	+	0.353328i
$201$	−291.708	−	23.9807i	−1.45128	−	0.119307i
$202$	−112.859	+	112.859i	−0.558707	+	0.558707i
$203$	−159.024	+	120.648i	−0.783370	+	0.594326i
$204$	−14.0192	+	170.533i	−0.0687214	+	0.835945i
$205$	−174.133	−	75.7999i	−0.849431	−	0.369755i
$206$	165.177			0.801828
$207$	−27.7451	+	19.8641i	−0.134034	+	0.0959619i
$208$	13.9267	+	13.9267i	0.0669552	+	0.0669552i
$209$		−	385.757i		−	1.84573i
$210$	−23.1367	−	146.679i	−0.110175	−	0.698471i
$211$	29.3640			0.139166			0.0695828	−	0.997576i	$-0.477833\pi$
$211$	29.3640			0.139166			0.0695828	+	0.997576i	$0.477833\pi$
$212$	94.9868	−	94.9868i	0.448051	−	0.448051i
$213$	127.987	+	150.915i	0.600876	+	0.708519i
$214$		−	251.108i		−	1.17340i
$215$	274.928	−	108.167i	1.27873	−	0.503104i
$216$	−18.6027	+	74.0671i	−0.0861238	+	0.342903i
$217$	66.2185	+	87.2814i	0.305154	+	0.402218i
$218$	−1.60754	−	1.60754i	−0.00737405	−	0.00737405i
$219$	−27.5302	−	2.26320i	−0.125709	−	0.0103342i
$220$	−133.910	−	58.2907i	−0.608681	−	0.264958i
$221$		−	140.418i		−	0.635375i
$222$	35.2279	−	29.8759i	0.158684	−	0.134576i
$223$	−203.552	−	203.552i	−0.912788	−	0.912788i	0.0837032	−	0.996491i	$-0.473325\pi$
$223$	−203.552	−	203.552i	−0.912788	−	0.912788i	−0.996491	+	0.0837032i	$0.973325\pi$
$224$	5.38310	−	39.2304i	0.0240317	−	0.175136i
$225$	187.507	−	124.363i	0.833365	−	0.552723i
$226$	283.011			1.25226
$227$	−152.211	−	152.211i	−0.670535	−	0.670535i	0.287305	−	0.957839i	$-0.407241\pi$
$227$	−152.211	−	152.211i	−0.670535	−	0.670535i	−0.957839	+	0.287305i	$0.907241\pi$
$228$	102.504	+	120.866i	0.449577	+	0.530116i
$229$	219.445			0.958275			0.479138	−	0.877740i	$-0.340949\pi$
$229$	219.445			0.958275			0.479138	+	0.877740i	$0.340949\pi$
$230$	24.5815	+	10.7003i	0.106876	+	0.0465230i
$231$	299.413	+	66.4486i	1.29616	+	0.287656i
$232$	−57.0318	−	57.0318i	−0.245827	−	0.245827i
$233$	−216.913	−	216.913i	−0.930957	−	0.930957i	0.0668091	−	0.997766i	$-0.478718\pi$
$233$	−216.913	−	216.913i	−0.930957	−	0.930957i	−0.997766	+	0.0668091i	$0.978718\pi$
$234$	10.2348	−	61.8287i	0.0437385	−	0.264225i
$235$	−54.5791	−	138.723i	−0.232251	−	0.590311i
$236$	−123.318			−0.522533
$237$	82.9128	+	97.7660i	0.349843	+	0.412515i
$238$	−224.911	+	170.635i	−0.945003	+	0.716953i
$239$	−261.894			−1.09579			−0.547896	−	0.836547i	$-0.684571\pi$
$239$	−261.894			−1.09579			−0.547896	+	0.836547i	$0.684571\pi$
$240$	57.4461	−	17.3189i	0.239359	−	0.0721619i
$241$			187.969i			0.779955i	0.920824	+	0.389978i	$0.127517\pi$
$241$			187.969i			0.779955i	−0.920824	+	0.389978i	$0.872483\pi$
$242$	92.2966	−	92.2966i	0.381391	−	0.381391i
$243$	226.088	−	89.0676i	0.930405	−	0.366533i
$244$	108.355			0.444080
$245$	154.681	−	189.997i	0.631350	−	0.775498i
$246$	−13.2032	+	160.607i	−0.0536715	+	0.652875i
$247$	−91.9622	−	91.9622i	−0.372317	−	0.372317i
$248$	−31.3023	+	31.3023i	−0.126219	+	0.126219i
$249$	3.31135	−	40.2801i	0.0132986	−	0.161768i
$250$	−159.463	−	76.2997i	−0.637851	−	0.305199i
$251$	−406.255			−1.61855			−0.809273	−	0.587433i	$-0.800139\pi$
$251$	−406.255			−1.61855			−0.809273	+	0.587433i	$0.800139\pi$
$252$	−111.470	+	58.7406i	−0.442341	+	0.233098i
$253$	−39.1544	+	39.1544i	−0.154760	+	0.154760i
$254$	79.0332			0.311154
$255$	−376.914	−	202.294i	−1.47809	−	0.793311i
$256$	16.0000			0.0625000
$257$	55.7465	+	55.7465i	0.216912	+	0.216912i	0.807196	−	0.590284i	$-0.200984\pi$
$257$	55.7465	+	55.7465i	0.216912	+	0.216912i	−0.590284	+	0.807196i	$0.700984\pi$
$258$	−162.145	−	191.192i	−0.628469	−	0.741055i
$259$	75.5032	+	10.3604i	0.291518	+	0.0400014i
$260$	−45.8195	+	18.0272i	−0.176229	+	0.0693353i
$261$	−41.9130	+	253.197i	−0.160586	+	0.970105i
$262$	−122.046	+	122.046i	−0.465826	+	0.465826i
$263$	96.5716	+	96.5716i	0.367192	+	0.367192i	0.866452	−	0.499260i	$-0.166395\pi$
$263$	96.5716	+	96.5716i	0.367192	+	0.367192i	−0.499260	+	0.866452i	$0.666395\pi$
$264$	−10.1534	+	123.508i	−0.0384597	+	0.467834i
$265$	122.954	+	312.512i	0.463978	+	1.17929i
$266$	−35.5463	+	259.050i	−0.133633	+	0.973873i
$267$	−37.6105	−	44.3481i	−0.140863	−	0.166098i
$268$	137.976	−	137.976i	0.514837	−	0.514837i
$269$		−	100.672i		−	0.374246i	−0.982336	−	0.187123i	$-0.940084\pi$
$269$		−	100.672i		−	0.374246i	0.982336	−	0.187123i	$-0.0599163\pi$
$270$	−151.218	−	116.547i	−0.560066	−	0.431655i
$271$			299.070i			1.10358i	0.833983	+	0.551790i	$0.186055\pi$
$271$			299.070i			1.10358i	−0.833983	+	0.551790i	$0.813945\pi$
$272$	−80.6611	−	80.6611i	−0.296548	−	0.296548i
$273$	87.2194	−	55.5375i	0.319485	−	0.203434i
$274$			283.898i			1.03612i
$275$	267.233	−	248.791i	0.971756	−	0.904695i
$276$	1.86383	−	22.6721i	0.00675301	−	0.0821454i
$277$	−310.502	−	310.502i	−1.12095	−	1.12095i	−0.991599	−	0.129348i	$-0.958712\pi$
$277$	−310.502	−	310.502i	−1.12095	−	1.12095i	−0.129348	−	0.991599i	$-0.541288\pi$
$278$	−41.4554	+	41.4554i	−0.149120	+	0.149120i
$279$	138.969	+	23.0042i	0.498097	+	0.0824523i
$280$	84.5542	+	51.4838i	0.301979	+	0.183871i
$281$		−	229.692i		−	0.817409i	−0.912667	−	0.408704i	$-0.865981\pi$
$281$		−	229.692i		−	0.817409i	0.912667	−	0.408704i	$-0.134019\pi$
$282$	−96.4718	+	81.8152i	−0.342099	+	0.290125i
$283$	170.587	+	170.587i	0.602781	+	0.602781i	0.941049	−	0.338269i	$-0.109841\pi$
$283$	170.587	+	170.587i	0.602781	+	0.602781i	−0.338269	+	0.941049i	$0.609841\pi$
$284$	−131.919			−0.464503
$285$	−379.334	+	114.362i	−1.33100	+	0.401269i
$286$		−	101.697i		−	0.355585i
$287$	−211.820	+	160.703i	−0.738049	+	0.559942i
$288$	−29.6374	−	41.3959i	−0.102908	−	0.143736i
$289$			524.277i			1.81411i
$290$	187.637	−	73.8239i	0.647026	−	0.254565i
$291$	29.4211	−	357.886i	0.101103	−	1.22985i
$292$	13.0216	−	13.0216i	0.0445946	−	0.0445946i
$293$	−186.419	+	186.419i	−0.636243	+	0.636243i	−0.949627	−	0.313384i	$-0.898537\pi$
$293$	−186.419	+	186.419i	−0.636243	+	0.636243i	0.313384	+	0.949627i	$0.398537\pi$
$294$	−194.944	−	72.2127i	−0.663076	−	0.245622i
$295$	123.047	−	282.674i	0.417110	−	0.958218i
$296$			30.7938i			0.104033i
$297$	338.353	−	202.510i	1.13924	−	0.681851i
$298$	−189.375	+	189.375i	−0.635485	+	0.635485i
$299$			18.6684i			0.0624360i
$300$	−17.6212	+	148.961i	−0.0587374	+	0.496538i
$301$	56.2287	−	409.778i	0.186806	−	1.36139i
$302$	117.328	−	117.328i	0.388503	−	0.388503i
$303$	−258.220	+	218.990i	−0.852211	+	0.722738i
$304$	−105.653			−0.347542
$305$	−108.118	+	248.377i	−0.354485	+	0.814351i
$306$	−59.2783	+	358.102i	−0.193720	+	1.17027i
$307$	−9.77168	+	9.77168i	−0.0318296	+	0.0318296i	−0.722842	−	0.691013i	$-0.757165\pi$
$307$	−9.77168	+	9.77168i	−0.0318296	+	0.0318296i	0.691013	+	0.722842i	$0.257165\pi$
$308$	−162.891	+	123.582i	−0.528868	+	0.401241i
$309$	349.215	+	28.7082i	1.13014	+	0.0929069i
$310$	−40.5187	−	102.986i	−0.130706	−	0.332213i
$311$	145.632			0.468271			0.234136	−	0.972204i	$-0.424774\pi$
$311$	145.632			0.468271			0.234136	+	0.972204i	$0.424774\pi$
$312$	27.0231	+	31.8641i	0.0866126	+	0.102129i
$313$	354.096	+	354.096i	1.13130	+	1.13130i	0.989962	+	0.141335i	$0.0451395\pi$
$313$	354.096	+	354.096i	1.13130	+	1.13130i	0.141335	+	0.989962i	$0.454861\pi$
$314$		−	247.008i		−	0.786651i
$315$	−23.4220	−	314.128i	−0.0743556	−	0.997232i
$316$	−85.4601			−0.270443
$317$	−136.486	+	136.486i	−0.430556	+	0.430556i	−0.888817	−	0.458262i	$-0.848472\pi$
$317$	−136.486	+	136.486i	−0.430556	+	0.430556i	0.458262	+	0.888817i	$0.348472\pi$
$318$	217.329	−	184.311i	0.683425	−	0.579594i
$319$			416.465i			1.30553i
$320$	−15.9649	+	36.6759i	−0.0498904	+	0.114612i
$321$	43.6435	−	530.891i	0.135961	−	1.65386i
$322$	29.9016	−	22.6857i	0.0928621	−	0.0704525i
$323$	532.630	+	532.630i	1.64901	+	1.64901i
$324$	−52.2028	+	153.359i	−0.161120	+	0.473329i
$325$	4.39643	−	123.017i	0.0135275	−	0.378514i
$326$		−	347.083i		−	1.06467i
$327$	−3.11925	−	3.67804i	−0.00953899	−	0.0112478i
$328$	−75.9663	−	75.9663i	−0.231605	−	0.231605i
$329$	−206.766	−	28.3719i	−0.628467	−	0.0862368i
$330$	−272.980	−	146.511i	−0.827211	−	0.443974i
$331$	317.945			0.960559			0.480279	−	0.877116i	$-0.340535\pi$
$331$	317.945			0.960559			0.480279	+	0.877116i	$0.340535\pi$
$332$	19.0523	+	19.0523i	0.0573864	+	0.0573864i
$333$	79.6710	−	57.0405i	0.239252	−	0.171293i
$334$	−65.2042			−0.195222
$335$	178.601	+	453.949i	0.533138	+	1.35507i
$336$	18.1993	−	82.0048i	0.0541644	−	0.244062i
$337$	95.8647	+	95.8647i	0.284465	+	0.284465i	0.834887	−	0.550422i	$-0.185533\pi$
$337$	95.8647	+	95.8647i	0.284465	+	0.284465i	−0.550422	+	0.834887i	$0.685533\pi$
$338$	144.756	+	144.756i	0.428272	+	0.428272i
$339$	598.338	+	49.1882i	1.76501	+	0.145098i
$340$	265.379	−	104.411i	0.780527	−	0.307090i
$341$	228.580			0.670322
$342$	195.705	+	273.350i	0.572237	+	0.799269i
$343$	−126.046	−	319.001i	−0.367482	−	0.930031i
$344$	167.127			0.485833
$345$	50.1103	+	26.8948i	0.145247	+	0.0779559i
$346$		−	244.193i		−	0.705761i
$347$	−76.3053	+	76.3053i	−0.219900	+	0.219900i	−0.808456	−	0.588556i	$-0.799697\pi$
$347$	−76.3053	+	76.3053i	−0.219900	+	0.219900i	0.588556	+	0.808456i	$0.299697\pi$
$348$	−110.664	−	130.488i	−0.317999	−	0.374966i
$349$	−27.7850			−0.0796133			−0.0398067	−	0.999207i	$-0.512674\pi$
$349$	−27.7850			−0.0796133			−0.0398067	+	0.999207i	$0.512674\pi$
$350$	−202.382	+	142.448i	−0.578235	+	0.406994i
$351$	32.3843	−	128.939i	0.0922630	−	0.367347i
$352$	−58.4187	−	58.4187i	−0.165962	−	0.165962i
$353$	−188.774	+	188.774i	−0.534769	+	0.534769i	−0.921988	−	0.387218i	$-0.873436\pi$
$353$	−188.774	+	188.774i	−0.534769	+	0.534769i	0.387218	+	0.921988i	$0.373436\pi$
$354$	−260.717	−	21.4330i	−0.736488	−	0.0605452i
$355$	131.630	−	302.390i	0.370788	−	0.851803i
$356$	38.7660			0.108893
$357$	−505.161	+	321.664i	−1.41502	+	0.901020i
$358$	48.8414	−	48.8414i	0.136429	−	0.136429i
$359$	171.974			0.479037			0.239519	−	0.970892i	$-0.423010\pi$
$359$	171.974			0.479037			0.239519	+	0.970892i	$0.423010\pi$
$360$	124.462	−	26.6310i	0.345728	−	0.0739750i
$361$	336.659			0.932572
$362$	−74.5578	−	74.5578i	−0.205961	−	0.205961i
$363$	211.174	−	179.091i	0.581746	−	0.493364i
$364$	−9.37109	+	68.2936i	−0.0257448	+	0.187620i
$365$	16.8556	+	42.8418i	0.0461798	+	0.117375i
$366$	229.084	+	18.8325i	0.625912	+	0.0514550i
$367$	−181.555	+	181.555i	−0.494700	+	0.494700i	−0.909784	−	0.415083i	$-0.863753\pi$
$367$	−181.555	+	181.555i	−0.494700	+	0.494700i	0.415083	+	0.909784i	$0.363753\pi$
$368$	10.7238	+	10.7238i	0.0291407	+	0.0291407i
$369$	−55.8281	+	337.259i	−0.151296	+	0.913981i
$370$	−70.5868	−	30.7263i	−0.190775	−	0.0830440i
$371$	465.796	+	63.9154i	1.25552	+	0.172279i
$372$	−71.6193	+	60.7384i	−0.192525	+	0.163275i
$373$	−104.153	+	104.153i	−0.279231	+	0.279231i	−0.832802	−	0.553571i	$-0.813265\pi$
$373$	−104.153	+	104.153i	−0.279231	+	0.279231i	0.553571	+	0.832802i	$0.313265\pi$
$374$			589.015i			1.57491i
$375$	−323.873	−	189.027i	−0.863662	−	0.504072i
$376$		−	84.3288i		−	0.224279i
$377$	99.2830	+	99.2830i	0.263350	+	0.263350i
$378$	−245.878	+	104.815i	−0.650470	+	0.277288i
$379$		−	339.431i		−	0.895596i	−0.894135	−	0.447798i	$-0.852208\pi$
$379$		−	339.431i		−	0.895596i	0.894135	−	0.447798i	$-0.147792\pi$
$380$	105.421	−	242.182i	0.277425	−	0.637321i
$381$	167.091	+	13.7362i	0.438559	+	0.0360531i
$382$	22.0006	+	22.0006i	0.0575933	+	0.0575933i
$383$	187.161	−	187.161i	0.488670	−	0.488670i	−0.419217	−	0.907886i	$-0.637695\pi$
$383$	187.161	−	187.161i	0.488670	−	0.488670i	0.907886	+	0.419217i	$0.137695\pi$
$384$	33.8270	+	2.78085i	0.0880912	+	0.00724180i
$385$	−120.746	−	496.698i	−0.313626	−	1.29012i
$386$		−	147.532i		−	0.382207i
$387$	−309.575	−	432.398i	−0.799937	−	1.11731i
$388$	169.278	+	169.278i	0.436284	+	0.436284i
$389$	−511.312			−1.31443			−0.657214	−	0.753704i	$-0.728265\pi$
$389$	−511.312			−1.31443			−0.657214	+	0.753704i	$0.728265\pi$
$390$	−100.004	+	30.1493i	−0.256421	+	0.0773059i
$391$		−	108.124i		−	0.276532i
$392$	120.775	−	67.9801i	0.308101	−	0.173419i
$393$	−279.241	+	236.817i	−0.710537	+	0.602588i
$394$		−	248.960i		−	0.631878i
$395$	85.2729	−	195.895i	0.215881	−	0.495938i
$396$	−42.9322	+	259.355i	−0.108415	+	0.654936i
$397$	448.583	−	448.583i	1.12993	−	1.12993i	0.139744	−	0.990188i	$-0.455372\pi$
$397$	448.583	−	448.583i	1.12993	−	1.12993i	0.990188	−	0.139744i	$-0.0446280\pi$
$398$	324.188	−	324.188i	0.814542	−	0.814542i
$399$	−120.175	+	541.503i	−0.301191	+	1.35715i
$400$	−68.1401	−	73.1910i	−0.170350	−	0.182978i
$401$			44.3430i			0.110581i	0.998470	+	0.0552905i	$0.0176085\pi$
$401$			44.3430i			0.110581i	−0.998470	+	0.0552905i	$0.982391\pi$
$402$	315.689	−	267.727i	0.785295	−	0.665988i
$403$	54.4921	−	54.4921i	0.135216	−	0.135216i
$404$		−	225.718i		−	0.558707i
$405$	−299.447	−	272.684i	−0.739375	−	0.673294i
$406$	38.3760	−	279.672i	0.0945221	−	0.688848i
$407$	112.433	−	112.433i	0.276249	−	0.276249i
$408$	−156.514	−	184.552i	−0.383612	−	0.452333i
$409$	−392.358			−0.959311			−0.479656	−	0.877457i	$-0.659238\pi$
$409$	−392.358			−0.959311			−0.479656	+	0.877457i	$0.659238\pi$
$410$	249.933	−	98.3335i	0.609593	−	0.239838i
$411$	−49.3423	+	600.213i	−0.120054	+	1.46037i
$412$	−165.177	+	165.177i	−0.400914	+	0.400914i
$413$	−260.873	−	343.852i	−0.631654	−	0.832571i
$414$	7.88097	−	47.6092i	0.0190362	−	0.114998i
$415$	−62.6830	+	24.6619i	−0.151043	+	0.0594263i
$416$	−27.8534			−0.0669552
$417$	−94.8495	+	80.4394i	−0.227457	+	0.192900i
$418$	385.757	+	385.757i	0.922863	+	0.922863i
$419$			383.324i			0.914855i	0.889247	+	0.457427i	$0.151229\pi$
$419$			383.324i			0.914855i	−0.889247	+	0.457427i	$0.848771\pi$
$420$	169.816	+	123.542i	0.404323	+	0.294148i
$421$	809.373			1.92250			0.961250	−	0.275678i	$-0.0889023\pi$
$421$	809.373			1.92250			0.961250	+	0.275678i	$0.0889023\pi$
$422$	−29.3640	+	29.3640i	−0.0695828	+	0.0695828i
$423$	−218.179	+	156.206i	−0.515791	+	0.369281i
$424$			189.974i			0.448051i
$425$	−25.4634	+	712.495i	−0.0599139	+	1.67646i
$426$	−278.901	−	22.9279i	−0.654698	−	0.0538214i
$427$	229.221	+	302.132i	0.536817	+	0.707569i
$428$	251.108	+	251.108i	0.586702	+	0.586702i
$429$	17.6753	−	215.007i	0.0412012	−	0.501183i
$430$	−166.760	+	383.095i	−0.387815	+	0.890919i
$431$			432.674i			1.00388i	0.864902	+	0.501942i	$0.167381\pi$
$431$			432.674i			1.00388i	−0.864902	+	0.501942i	$0.832619\pi$
$432$	−55.4644	−	92.6699i	−0.128390	−	0.214514i
$433$	−288.449	−	288.449i	−0.666163	−	0.666163i	0.290662	−	0.956826i	$-0.406124\pi$
$433$	−288.449	−	288.449i	−0.666163	−	0.666163i	−0.956826	+	0.290662i	$0.906124\pi$
$434$	−153.500	−	21.0629i	−0.353686	−	0.0485320i
$435$	409.532	−	123.466i	0.941452	−	0.283829i
$436$	3.21508			0.00737405
$437$	−70.8125	−	70.8125i	−0.162042	−	0.162042i
$438$	29.7934	−	25.2670i	0.0680214	−	0.0576871i
$439$	−652.665			−1.48671			−0.743354	−	0.668898i	$-0.766766\pi$
$439$	−652.665			−1.48671			−0.743354	+	0.668898i	$0.766766\pi$
$440$	192.201	−	75.6192i	0.436819	−	0.171862i
$441$	−399.598	−	186.553i	−0.906119	−	0.423023i
$442$	140.418	+	140.418i	0.317687	+	0.317687i
$443$	429.708	+	429.708i	0.969996	+	0.969996i	0.999563	−	0.0295673i	$-0.00941292\pi$
$443$	429.708	+	429.708i	0.969996	+	0.969996i	−0.0295673	+	0.999563i	$0.509413\pi$
$444$	−5.35206	+	65.1038i	−0.0120542	+	0.146630i
$445$	−38.6810	+	88.8610i	−0.0869236	+	0.199688i
$446$	407.103			0.912788
$447$	−433.287	+	367.460i	−0.969323	+	0.822057i
$448$	33.8473	+	44.6135i	0.0755519	+	0.0995836i
$449$	544.342			1.21234			0.606171	−	0.795334i	$-0.292705\pi$
$449$	544.342			1.21234			0.606171	+	0.795334i	$0.292705\pi$
$450$	−63.1445	+	311.870i	−0.140321	+	0.693044i
$451$			554.732i			1.23000i
$452$	−283.011	+	283.011i	−0.626130	+	0.626130i
$453$	268.446	−	227.662i	0.592595	−	0.502564i
$454$	304.423			0.670535
$455$	−147.195	−	89.6248i	−0.323506	−	0.196978i
$456$	−223.370	−	18.3628i	−0.489847	−	0.0402693i
$457$	−100.300	−	100.300i	−0.219475	−	0.219475i	0.588802	−	0.808277i	$-0.299600\pi$
$457$	−100.300	−	100.300i	−0.219475	−	0.219475i	−0.808277	+	0.588802i	$0.799600\pi$
$458$	−219.445	+	219.445i	−0.479138	+	0.479138i
$459$	−187.565	+	746.792i	−0.408638	+	1.62700i
$460$	−35.2818	+	13.8812i	−0.0766996	+	0.0301766i
$461$	16.3102			0.0353801			0.0176900	−	0.999844i	$-0.494369\pi$
$461$	16.3102			0.0353801			0.0176900	+	0.999844i	$0.494369\pi$
$462$	−365.862	+	232.965i	−0.791909	+	0.504253i
$463$	−401.469	+	401.469i	−0.867104	+	0.867104i	−0.992151	−	0.125047i	$-0.960092\pi$
$463$	−401.469	+	401.469i	−0.867104	+	0.867104i	0.125047	+	0.992151i	$0.460092\pi$
$464$	114.064			0.245827
$465$	−67.7649	−	224.774i	−0.145731	−	0.483385i
$466$	433.826			0.930957
$467$	−371.481	−	371.481i	−0.795462	−	0.795462i	0.186914	−	0.982376i	$-0.440151\pi$
$467$	−371.481	−	371.481i	−0.795462	−	0.795462i	−0.982376	+	0.186914i	$0.940151\pi$
$468$	51.5939	+	72.0635i	0.110243	+	0.153982i
$469$	676.608	+	92.8425i	1.44266	+	0.197959i
$470$	193.302	+	84.1441i	0.411281	+	0.179030i
$471$	42.9309	−	522.222i	0.0911483	−	1.10875i
$472$	123.318	−	123.318i	0.261266	−	0.261266i
$473$	−610.208	−	610.208i	−1.29008	−	1.29008i
$474$	−180.679	−	14.8532i	−0.381179	−	0.0313360i
$475$	449.950	+	483.303i	0.947263	+	1.01748i
$476$	54.2759	−	395.546i	0.114025	−	0.830978i
$477$	491.508	−	351.896i	1.03042	−	0.737727i
$478$	261.894	−	261.894i	0.547896	−	0.547896i
$479$		−	615.307i		−	1.28457i	−0.766467	−	0.642283i	$-0.777987\pi$
$479$		−	615.307i		−	1.28457i	0.766467	−	0.642283i	$-0.222013\pi$
$480$	−40.1273	+	74.7650i	−0.0835985	+	0.155760i
$481$		−	53.6069i		−	0.111449i
$482$	−187.969	−	187.969i	−0.389978	−	0.389978i
$483$	67.1605	−	42.7648i	0.139049	−	0.0885400i
$484$			184.593i			0.381391i
$485$	−556.934	+	219.119i	−1.14832	+	0.451793i
$486$	−137.021	+	315.156i	−0.281936	+	0.648469i
$487$	597.102	+	597.102i	1.22608	+	1.22608i	0.965434	+	0.260649i	$0.0839364\pi$
$487$	597.102	+	597.102i	1.22608	+	1.22608i	0.260649	+	0.965434i	$0.416064\pi$
$488$	−108.355	+	108.355i	−0.222040	+	0.222040i
$489$	60.3241	−	733.798i	0.123362	−	1.50061i
$490$	35.3163	+	344.678i	0.0720740	+	0.703424i
$491$			11.7151i			0.0238597i	0.999929	+	0.0119298i	$0.00379747\pi$
$491$			11.7151i			0.0238597i	−0.999929	+	0.0119298i	$0.996203\pi$
$492$	−147.404	−	173.810i	−0.299602	−	0.353273i
$493$	−575.031	−	575.031i	−1.16639	−	1.16639i
$494$	183.924			0.372317
$495$	−551.666	−	357.198i	−1.11448	−	0.721611i
$496$		−	62.6045i		−	0.126219i
$497$	−279.068	−	367.835i	−0.561506	−	0.740110i
$498$	36.9688	+	43.5915i	0.0742345	+	0.0875330i
$499$		−	11.1783i		−	0.0224014i	−0.999937	−	0.0112007i	$-0.996435\pi$
$499$		−	11.1783i		−	0.0224014i	0.999937	−	0.0112007i	$-0.00356537\pi$
$500$	235.762	−	83.1630i	0.471525	−	0.166326i
$501$	−137.854	−	11.3327i	−0.275157	−	0.0226201i
$502$	406.255	−	406.255i	0.809273	−	0.809273i
$503$	−15.0212	+	15.0212i	−0.0298632	+	0.0298632i	−0.721881	−	0.692017i	$-0.756722\pi$
$503$	−15.0212	+	15.0212i	−0.0298632	+	0.0298632i	0.692017	+	0.721881i	$0.256722\pi$
$504$	52.7293	−	170.211i	0.104622	−	0.337719i
$505$	517.400	+	225.223i	1.02455	+	0.445986i
$506$		−	78.3088i		−	0.154760i
$507$	280.882	+	331.200i	0.554008	+	0.653255i
$508$	−79.0332	+	79.0332i	−0.155577	+	0.155577i
$509$		−	62.6374i		−	0.123060i	−0.998105	−	0.0615298i	$-0.980402\pi$
$509$		−	62.6374i		−	0.123060i	0.998105	−	0.0615298i	$-0.0195979\pi$
$510$	579.209	−	174.620i	1.13570	−	0.342392i
$511$	63.8554	+	8.76209i	0.124962	+	0.0171469i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	366.248	+	611.928i	0.713934	+	1.19284i
$514$	−111.493			−0.216912
$515$	−213.810	−	543.440i	−0.415166	−	1.05522i
$516$	353.337	+	29.0472i	0.684762	+	0.0562930i
$517$	−307.899	+	307.899i	−0.595549	+	0.595549i
$518$	−85.8636	+	65.1428i	−0.165760	+	0.125758i
$519$	42.4416	−	516.271i	0.0817757	−	0.994741i
$520$	27.7923	−	63.8467i	0.0534468	−	0.122782i
$521$	−2.86685			−0.00550258			−0.00275129	−	0.999996i	$-0.500876\pi$
$521$	−2.86685			−0.00550258			−0.00275129	+	0.999996i	$0.500876\pi$
$522$	−211.284	−	295.110i	−0.404759	−	0.565345i
$523$	216.205	+	216.205i	0.413394	+	0.413394i	0.882919	−	0.469525i	$-0.155575\pi$
$523$	216.205	+	216.205i	0.413394	+	0.413394i	−0.469525	+	0.882919i	$0.655575\pi$
$524$		−	244.093i		−	0.465826i
$525$	−452.632	+	265.987i	−0.862157	+	0.506642i
$526$	−193.143			−0.367192
$527$	−315.609	+	315.609i	−0.598879	+	0.598879i
$528$	−113.355	−	133.662i	−0.214687	−	0.253147i
$529$		−	514.625i		−	0.972826i
$530$	−435.466	−	189.557i	−0.821634	−	0.357655i
$531$	−547.479	−	90.6269i	−1.03103	−	0.170672i
$532$	−223.504	−	294.596i	−0.420120	−	0.553753i
$533$	132.245	+	132.245i	0.248114	+	0.248114i
$534$	81.9586	+	6.73765i	0.153480	+	0.0126173i
$535$	−826.160	+	325.043i	−1.54422	+	0.607558i
$536$			275.953i			0.514837i
$537$	111.749	−	94.7712i	0.208098	−	0.176483i
$538$	100.672	+	100.672i	0.187123	+	0.187123i
$539$	−689.179	−	192.764i	−1.27862	−	0.357633i
$540$	267.765	−	34.6710i	0.495861	−	0.0642056i
$541$	−544.738			−1.00691			−0.503454	−	0.864022i	$-0.667938\pi$
$541$	−544.738			−1.00691			−0.503454	+	0.864022i	$0.667938\pi$
$542$	−299.070	−	299.070i	−0.551790	−	0.551790i
$543$	−144.671	−	170.588i	−0.266429	−	0.314158i
$544$	161.322			0.296548
$545$	−3.20804	+	7.36976i	−0.00588631	+	0.0135225i
$546$	−31.6819	+	142.757i	−0.0580255	+	0.261460i
$547$	−644.286	−	644.286i	−1.17785	−	1.17785i	−0.980290	−	0.197564i	$-0.936697\pi$
$547$	−644.286	−	644.286i	−1.17785	−	1.17785i	−0.197564	−	0.980290i	$-0.563303\pi$
$548$	−283.898	−	283.898i	−0.518061	−	0.518061i
$549$	481.053	+	79.6310i	0.876235	+	0.145047i
$550$	−18.4418	+	516.024i	−0.0335306	+	0.938225i
$551$	−753.197			−1.36696
$552$	20.8083	+	24.5359i	0.0376962	+	0.0444492i
$553$	−180.787	−	238.292i	−0.326921	−	0.430908i
$554$	621.005			1.12095
$555$	−143.893	−	77.2294i	−0.259268	−	0.139152i
$556$		−	82.9107i		−	0.149120i
$557$	180.720	−	180.720i	0.324452	−	0.324452i	−0.526020	−	0.850472i	$-0.676316\pi$
$557$	180.720	−	180.720i	0.324452	−	0.324452i	0.850472	+	0.526020i	$0.176316\pi$
$558$	−161.973	+	115.965i	−0.290275	+	0.207822i
$559$	−290.940			−0.520465
$560$	−136.038	+	33.0705i	−0.242925	+	0.0590544i
$561$	−102.373	+	1245.29i	−0.182482	+	2.21977i
$562$	229.692	+	229.692i	0.408704	+	0.408704i
$563$	16.4783	−	16.4783i	0.0292687	−	0.0292687i	−0.692321	−	0.721590i	$-0.743412\pi$
$563$	16.4783	−	16.4783i	0.0292687	−	0.0292687i	0.721590	+	0.692321i	$0.243412\pi$
$564$	14.6566	−	178.287i	0.0259869	−	0.316112i
$565$	−366.339	−	931.120i	−0.648388	−	1.64800i
$566$	−341.174			−0.602781
$567$	−538.049	+	178.864i	−0.948940	+	0.315457i
$568$	131.919	−	131.919i	0.232251	−	0.232251i
$569$	354.571			0.623147			0.311574	−	0.950222i	$-0.399144\pi$
$569$	354.571			0.623147			0.311574	+	0.950222i	$0.399144\pi$
$570$	264.973	−	493.696i	0.464864	−	0.866133i
$571$	−110.075			−0.192777			−0.0963883	−	0.995344i	$-0.530729\pi$
$571$	−110.075			−0.192777			−0.0963883	+	0.995344i	$0.530729\pi$
$572$	101.697	+	101.697i	0.177793	+	0.177793i
$573$	42.6897	+	50.3372i	0.0745021	+	0.0878486i
$574$	51.1168	−	372.524i	0.0890537	−	0.648996i
$575$	3.38533	−	94.7254i	0.00588752	−	0.164740i
$576$	71.0334	+	11.7585i	0.123322	+	0.0204140i
$577$	212.392	−	212.392i	0.368097	−	0.368097i	−0.498686	−	0.866783i	$-0.666184\pi$
$577$	212.392	−	212.392i	0.368097	−	0.368097i	0.866783	+	0.498686i	$0.166184\pi$
$578$	−524.277	−	524.277i	−0.907054	−	0.907054i
$579$	25.6415	−	311.910i	0.0442859	−	0.538705i
$580$	−113.814	+	261.461i	−0.196230	+	0.450795i
$581$	−12.8200	+	93.4285i	−0.0220655	+	0.160806i
$582$	328.465	+	387.307i	0.564372	+	0.665476i
$583$	693.626	−	693.626i	1.18975	−	1.18975i
$584$			26.0432i			0.0445946i
$585$	−216.668	+	46.3602i	−0.370373	+	0.0792482i
$586$		−	372.838i		−	0.636243i
$587$	277.047	+	277.047i	0.471972	+	0.471972i	0.902552	−	0.430580i	$-0.141691\pi$
$587$	277.047	+	277.047i	0.471972	+	0.471972i	−0.430580	+	0.902552i	$0.641691\pi$
$588$	267.157	−	122.732i	0.454349	−	0.208727i
$589$			413.397i			0.701862i
$590$	159.627	+	405.722i	0.270554	+	0.687664i
$591$	43.2700	−	526.348i	0.0732150	−	0.890606i
$592$	−30.7938	−	30.7938i	−0.0520165	−	0.0520165i
$593$	−118.407	+	118.407i	−0.199674	+	0.199674i	−0.799860	−	0.600186i	$-0.795093\pi$
$593$	−118.407	+	118.407i	−0.199674	+	0.199674i	0.600186	+	0.799860i	$0.295093\pi$
$594$	−135.844	+	540.863i	−0.228693	+	0.910544i
$595$	852.530	+	519.092i	1.43282	+	0.872424i
$596$		−	378.749i		−	0.635485i
$597$	741.739	−	629.049i	1.24244	−	1.05368i
$598$	−18.6684	−	18.6684i	−0.0312180	−	0.0312180i
$599$	−254.409			−0.424722			−0.212361	−	0.977191i	$-0.568115\pi$
$599$	−254.409			−0.424722			−0.212361	+	0.977191i	$0.568115\pi$
$600$	−131.340	−	166.583i	−0.218900	−	0.277638i
$601$		−	335.032i		−	0.557458i	−0.960370	−	0.278729i	$-0.910087\pi$
$601$		−	335.032i		−	0.557458i	0.960370	−	0.278729i	$-0.0899131\pi$
$602$	353.549	+	466.006i	0.587291	+	0.774097i
$603$	713.957	−	511.158i	1.18401	−	0.847692i
$604$			234.656i			0.388503i
$605$	−423.132	−	184.189i	−0.699393	−	0.304444i
$606$	39.2304	−	477.210i	0.0647367	−	0.787474i
$607$	537.196	−	537.196i	0.885002	−	0.885002i	−0.109036	−	0.994038i	$-0.534776\pi$
$607$	537.196	−	537.196i	0.885002	−	0.885002i	0.994038	+	0.109036i	$0.0347763\pi$
$608$	105.653	−	105.653i	0.173771	−	0.173771i
$609$	129.742	−	584.610i	0.213041	−	0.959950i
$610$	−140.259	−	356.495i	−0.229933	−	0.584418i
$611$			146.803i			0.240266i
$612$	−298.824	−	417.380i	−0.488274	−	0.681994i
$613$	−155.599	+	155.599i	−0.253832	+	0.253832i	−0.822540	−	0.568708i	$-0.807444\pi$
$613$	−155.599	+	155.599i	−0.253832	+	0.253832i	0.568708	+	0.822540i	$0.307444\pi$
$614$		−	19.5434i		−	0.0318296i
$615$	545.497	−	164.456i	0.886986	−	0.267409i
$616$	39.3092	−	286.473i	0.0638137	−	0.465054i
$617$	533.777	−	533.777i	0.865116	−	0.865116i	−0.126811	−	0.991927i	$-0.540474\pi$
$617$	533.777	−	533.777i	0.865116	−	0.865116i	0.991927	+	0.126811i	$0.0404741\pi$
$618$	−377.923	+	320.506i	−0.611526	+	0.518619i
$619$	−96.5213			−0.155931			−0.0779655	−	0.996956i	$-0.524842\pi$
$619$	−96.5213			−0.155931			−0.0779655	+	0.996956i	$0.524842\pi$
$620$	143.505	+	62.4673i	0.231459	+	0.100754i
$621$	24.9365	−	99.2851i	0.0401554	−	0.159879i
$622$	−145.632	+	145.632i	−0.234136	+	0.234136i
$623$	82.0076	+	108.093i	0.131633	+	0.173504i
$624$	−58.8873	−	4.84101i	−0.0943706	−	0.00775802i
$625$	−44.6159	+	623.406i	−0.0713855	+	0.997449i
$626$	−708.192			−1.13130
$627$	748.516	+	882.608i	1.19381	+	1.40767i
$628$	247.008	+	247.008i	0.393326	+	0.393326i
$629$			310.482i			0.493613i
$630$	337.550	+	290.706i	0.535794	+	0.461438i
$631$	−797.287			−1.26353			−0.631765	−	0.775160i	$-0.717669\pi$
$631$	−797.287			−1.26353			−0.631765	+	0.775160i	$0.717669\pi$
$632$	85.4601	−	85.4601i	0.135222	−	0.135222i
$633$	−67.1845	+	56.9774i	−0.106137	+	0.0900117i
$634$		−	272.972i		−	0.430556i
$635$	−102.303	−	260.023i	−0.161108	−	0.409485i
$636$	−33.0180	+	401.640i	−0.0519151	+	0.631510i
$637$	−210.250	+	118.342i	−0.330063	+	0.185781i
$638$	−416.465	−	416.465i	−0.652767	−	0.652767i
$639$	−585.665	−	96.9479i	−0.916533	−	0.151718i
$640$	−20.7110	−	52.6408i	−0.0323609	−	0.0822513i
$641$			816.250i			1.27340i	0.771111	+	0.636701i	$0.219701\pi$
$641$			816.250i			1.27340i	−0.771111	+	0.636701i	$0.780299\pi$
$642$	487.247	+	574.534i	0.758952	+	0.894913i
$643$	397.740	+	397.740i	0.618569	+	0.618569i	0.945164	−	0.326595i	$-0.105901\pi$
$643$	397.740	+	397.740i	0.618569	+	0.618569i	−0.326595	+	0.945164i	$0.605901\pi$
$644$	−7.21591	+	52.5873i	−0.0112048	+	0.0816573i
$645$	−419.146	+	780.952i	−0.649839	+	1.21078i
$646$	−1065.26			−1.64901
$647$	593.146	+	593.146i	0.916763	+	0.916763i	0.996792	−	0.0800295i	$-0.0255014\pi$
$647$	593.146	+	593.146i	0.916763	+	0.916763i	−0.0800295	+	0.996792i	$0.525501\pi$
$648$	−101.156	−	205.561i	−0.156105	−	0.317224i
$649$	−900.508			−1.38753
$650$	118.621	+	127.414i	0.182493	+	0.196021i
$651$	−320.867	−	71.2097i	−0.492883	−	0.109385i
$652$	347.083	+	347.083i	0.532335	+	0.532335i
$653$	−525.550	−	525.550i	−0.804824	−	0.804824i	0.179021	−	0.983845i	$-0.442707\pi$
$653$	−525.550	−	525.550i	−0.804824	−	0.804824i	−0.983845	+	0.179021i	$0.942707\pi$
$654$	6.79729	+	0.558792i	0.0103934	+	0.000854422i
$655$	559.520	+	243.558i	0.854229	+	0.371844i
$656$	151.933			0.231605
$657$	67.3803	−	48.2409i	0.102557	−	0.0734261i
$658$	235.138	−	178.394i	0.357352	−	0.271115i
$659$	415.401			0.630350			0.315175	−	0.949034i	$-0.397937\pi$
$659$	415.401			0.630350			0.315175	+	0.949034i	$0.397937\pi$
$660$	419.491	−	126.468i	0.635593	−	0.191618i
$661$			723.547i			1.09462i	0.836929	+	0.547312i	$0.184349\pi$
$661$			723.547i			1.09462i	−0.836929	+	0.547312i	$0.815651\pi$
$662$	−317.945	+	317.945i	−0.480279	+	0.480279i
$663$	272.465	+	321.275i	0.410957	+	0.484577i
$664$	−38.1046			−0.0573864
$665$	898.301	−	218.374i	1.35083	−	0.328383i
$666$	−22.6305	+	136.712i	−0.0339797	+	0.205273i
$667$	76.4496	+	76.4496i	0.114617	+	0.114617i
$668$	65.2042	−	65.2042i	0.0976110	−	0.0976110i
$669$	860.693	+	70.7559i	1.28654	+	0.105764i
$670$	−632.550	−	275.348i	−0.944105	−	0.410967i
$671$	791.248			1.17921
$672$	63.8055	+	100.204i	0.0949487	+	0.149113i
$673$	95.8909	−	95.8909i	0.142483	−	0.142483i	−0.632267	−	0.774750i	$-0.717876\pi$
$673$	95.8909	−	95.8909i	0.142483	−	0.142483i	0.774750	+	0.632267i	$0.217876\pi$
$674$	−191.729			−0.284465
$675$	−187.703	+	648.377i	−0.278079	+	0.960558i
$676$	−289.512			−0.428272
$677$	90.8203	+	90.8203i	0.134151	+	0.134151i	0.770994	−	0.636843i	$-0.219760\pi$
$677$	90.8203	+	90.8203i	0.134151	+	0.134151i	−0.636843	+	0.770994i	$0.719760\pi$
$678$	−647.526	+	549.150i	−0.955054	+	0.809956i
$679$	−113.905	+	830.106i	−0.167754	+	1.22254i
$680$	−160.969	+	369.790i	−0.236719	+	0.543808i
$681$	643.607	+	52.9096i	0.945091	+	0.0776940i
$682$	−228.580	+	228.580i	−0.335161	+	0.335161i
$683$	572.076	+	572.076i	0.837593	+	0.837593i	0.988542	−	0.150948i	$-0.0482327\pi$
$683$	572.076	+	572.076i	0.837593	+	0.837593i	−0.150948	+	0.988542i	$0.548233\pi$
$684$	−469.055	−	77.6449i	−0.685753	−	0.113516i
$685$	934.038	−	367.487i	1.36356	−	0.536477i
$686$	445.047	+	192.954i	0.648756	+	0.281274i
$687$	−502.088	+	425.808i	−0.730842	+	0.619808i
$688$	−167.127	+	167.127i	−0.242917	+	0.242917i
$689$		−	330.713i		−	0.479990i
$690$	−77.0050	+	23.2155i	−0.111602	+	0.0336456i
$691$			941.057i			1.36188i	0.732340	+	0.680939i	$0.238428\pi$
$691$			941.057i			1.36188i	−0.732340	+	0.680939i	$0.761572\pi$
$692$	244.193	+	244.193i	0.352880	+	0.352880i
$693$	−813.991	+	428.944i	−1.17459	+	0.618966i
$694$		−	152.611i		−	0.219900i
$695$	190.052	+	82.7290i	0.273455	+	0.119035i
$696$	241.152	+	19.8246i	0.346482	+	0.0284836i
$697$	−765.941	−	765.941i	−1.09891	−	1.09891i
$698$	27.7850	−	27.7850i	0.0398067	−	0.0398067i
$699$	917.189	+	75.4003i	1.31215	+	0.107869i
$700$	59.9344	−	344.830i	0.0856205	−	0.492615i
$701$		−	305.599i		−	0.435947i	−0.975955	−	0.217973i	$-0.930055\pi$
$701$		−	305.599i		−	0.435947i	0.975955	−	0.217973i	$-0.0699446\pi$
$702$	96.5544	+	161.323i	0.137542	+	0.229805i
$703$	203.341	+	203.341i	0.289247	+	0.289247i
$704$	116.837			0.165962
$705$	394.053	+	211.493i	0.558940	+	0.299990i
$706$		−	377.547i		−	0.534769i
$707$	629.378	−	477.495i	0.890209	−	0.675382i
$708$	282.150	−	239.284i	0.398517	−	0.337972i
$709$		−	976.020i		−	1.37661i	−0.725419	−	0.688307i	$-0.758354\pi$
$709$		−	976.020i		−	1.37661i	0.725419	−	0.688307i	$-0.241646\pi$
$710$	170.760	+	434.020i	0.240507	+	0.611295i
$711$	−379.408	−	62.8051i	−0.533625	−	0.0883335i
$712$	−38.7660	+	38.7660i	−0.0544466	+	0.0544466i
$713$	41.9599	−	41.9599i	0.0588497	−	0.0588497i
$714$	183.497	−	826.825i	0.256998	−	1.15802i
$715$	−334.590	+	131.641i	−0.467958	+	0.184113i
$716$			97.6829i			0.136429i
$717$	599.212	−	508.176i	0.835721	−	0.708753i
$718$	−171.974	+	171.974i	−0.239519	+	0.239519i
$719$			792.968i			1.10288i	0.834216	+	0.551438i	$0.185921\pi$
$719$			792.968i			1.10288i	−0.834216	+	0.551438i	$0.814079\pi$
$720$	−97.8310	+	151.093i	−0.135876	+	0.209851i
$721$	−809.993	−	111.145i	−1.12343	−	0.154154i
$722$	−336.659	+	336.659i	−0.466286	+	0.466286i
$723$	−364.733	−	430.072i	−0.504471	−	0.594844i
$724$	149.116			0.205961
$725$	−485.769	−	521.777i	−0.670026	−	0.719692i
$726$	−32.0829	+	390.265i	−0.0441913	+	0.537555i
$727$	−666.489	+	666.489i	−0.916767	+	0.916767i	−0.996793	−	0.0800261i	$-0.974500\pi$
$727$	−666.489	+	666.489i	−0.916767	+	0.916767i	0.0800261	+	0.996793i	$0.474500\pi$
$728$	−58.9226	−	77.6647i	−0.0809376	−	0.106682i
$729$	−344.463	+	642.484i	−0.472514	+	0.881323i
$730$	−59.6975	−	25.9862i	−0.0817773	−	0.0355975i
$731$	1685.08			2.30517
$732$	−247.916	+	210.251i	−0.338683	+	0.287228i
$733$	338.466	+	338.466i	0.461754	+	0.461754i	0.899230	−	0.437476i	$-0.144127\pi$
$733$	338.466	+	338.466i	0.461754	+	0.461754i	−0.437476	+	0.899230i	$0.644127\pi$
$734$		−	363.110i		−	0.494700i
$735$	14.7592	+	734.852i	0.0200805	+	0.999798i
$736$	−21.4476			−0.0291407
$737$	1007.55	−	1007.55i	1.36710	−	1.36710i
$738$	−281.431	−	393.087i	−0.381343	−	0.532638i
$739$		−	1021.49i		−	1.38226i	−0.722730	−	0.691130i	$-0.757113\pi$
$739$		−	1021.49i		−	1.38226i	0.722730	−	0.691130i	$-0.242887\pi$
$740$	101.313	−	39.8605i	0.136910	−	0.0538656i
$741$	388.851	+	31.9667i	0.524765	+	0.0431399i
$742$	−529.712	+	401.881i	−0.713897	+	0.541618i
$743$	262.382	+	262.382i	0.353138	+	0.353138i	0.861276	−	0.508138i	$-0.169666\pi$
$743$	262.382	+	262.382i	0.353138	+	0.353138i	−0.508138	+	0.861276i	$0.669666\pi$
$744$	10.8809	−	132.358i	0.0146248	−	0.177900i
$745$	868.185	+	377.919i	1.16535	+	0.507274i
$746$		−	208.307i		−	0.279231i
$747$	70.5826	+	98.5858i	0.0944881	+	0.131976i
$748$	−589.015	−	589.015i	−0.787453	−	0.787453i
$749$	−168.968	+	1231.38i	−0.225591	+	1.64404i
$750$	512.900	−	134.846i	0.683867	−	0.179795i
$751$	−429.513			−0.571922			−0.285961	−	0.958241i	$-0.592313\pi$
$751$	−429.513			−0.571922			−0.285961	+	0.958241i	$0.592313\pi$
$752$	84.3288	+	84.3288i	0.112139	+	0.112139i
$753$	929.508	−	788.291i	1.23441	−	1.04687i
$754$	−198.566			−0.263350
$755$	−537.889	−	234.142i	−0.712436	−	0.310122i
$756$	141.063	−	350.693i	0.186591	−	0.463879i
$757$	439.564	+	439.564i	0.580666	+	0.580666i	0.935086	−	0.354420i	$-0.115322\pi$
$757$	439.564	+	439.564i	0.580666	+	0.580666i	−0.354420	+	0.935086i	$0.615322\pi$
$758$	339.431	+	339.431i	0.447798	+	0.447798i
$759$	13.6103	−	165.559i	0.0179319	−	0.218128i
$760$	136.761	+	347.604i	0.179948	+	0.457373i
$761$	−1005.16			−1.32084			−0.660420	−	0.750897i	$-0.729622\pi$
$761$	−1005.16			−1.32084			−0.660420	+	0.750897i	$0.729622\pi$
$762$	−180.827	+	153.355i	−0.237306	+	0.201253i
$763$	6.80137	+	8.96476i	0.00891398	+	0.0117494i
$764$	−44.0013			−0.0575933
$765$	1254.91	−	268.511i	1.64040	−	0.350994i
$766$			374.321i			0.488670i
$767$	−214.676	+	214.676i	−0.279890	+	0.279890i
$768$	−36.6079	+	31.0462i	−0.0476665	+	0.0404247i
$769$	156.235			0.203167			0.101583	−	0.994827i	$-0.467609\pi$
$769$	156.235			0.203167			0.101583	+	0.994827i	$0.467609\pi$
$770$	617.444	+	375.952i	0.801875	+	0.488249i
$771$	−235.717	−	19.3778i	−0.305729	−	0.0251334i
$772$	147.532	+	147.532i	0.191104	+	0.191104i
$773$	95.1552	−	95.1552i	0.123099	−	0.123099i	−0.642874	−	0.765972i	$-0.722258\pi$
$773$	95.1552	−	95.1552i	0.123099	−	0.123099i	0.765972	+	0.642874i	$0.222258\pi$
$774$	741.973	+	122.822i	0.958622	+	0.158685i
$775$	−286.381	+	266.617i	−0.369523	+	0.344022i
$776$	−338.556			−0.436284
$777$	−192.854	+	122.801i	−0.248203	+	0.158045i
$778$	511.312	−	511.312i	0.657214	−	0.657214i
$779$	−1003.26			−1.28788
$780$	69.8550	−	130.154i	0.0895577	−	0.166864i
$781$	−963.316			−1.23344
$782$	108.124	+	108.124i	0.138266	+	0.138266i
$783$	−395.404	−	660.641i	−0.504986	−	0.843730i
$784$	−52.7953	+	188.756i	−0.0673409	+	0.240760i
$785$	−812.671	+	319.736i	−1.03525	+	0.407307i
$786$	42.4241	−	516.058i	0.0539747	−	0.656563i
$787$	909.207	−	909.207i	1.15528	−	1.15528i	0.169804	−	0.985478i	$-0.445687\pi$
$787$	909.207	−	909.207i	1.15528	−	1.15528i	0.985478	−	0.169804i	$-0.0543133\pi$
$788$	248.960	+	248.960i	0.315939	+	0.315939i
$789$	−408.341	−	33.5689i	−0.517543	−	0.0425462i
$790$	110.623	+	281.168i	0.140029	+	0.355909i
$791$	−1387.83	−	190.434i	−1.75452	−	0.240752i
$792$	−216.423	−	302.287i	−0.273261	−	0.381676i
$793$	188.629	−	188.629i	0.237868	−	0.237868i
$794$			897.166i			1.12993i
$795$	−887.711	−	476.445i	−1.11662	−	0.599302i
$796$			648.376i			0.814542i
$797$	8.09283	+	8.09283i	0.0101541	+	0.0101541i	0.712166	−	0.702011i	$-0.247715\pi$
$797$	8.09283	+	8.09283i	0.0101541	+	0.0101541i	−0.702011	+	0.712166i	$0.747715\pi$
$798$	−421.328	−	661.678i	−0.527979	−	0.829171i
$799$		−	850.257i		−	1.06415i
$800$	141.331	+	5.05094i	0.176664	+	0.00631367i
$801$	172.105	+	28.4893i	0.214862	+	0.0355672i
$802$	−44.3430	−	44.3430i	−0.0552905	−	0.0552905i
$803$	95.0883	−	95.0883i	0.118416	−	0.118416i
$804$	−47.9615	+	583.416i	−0.0596536	+	0.725642i
$805$	−113.343	−	69.0127i	−0.140798	−	0.0857300i
$806$			108.984i			0.135216i
$807$	195.343	+	230.337i	0.242061	+	0.285424i
$808$	225.718	+	225.718i	0.279353	+	0.279353i
$809$	1556.68			1.92421			0.962103	−	0.272686i	$-0.0879120\pi$
$809$	1556.68			1.92421			0.962103	+	0.272686i	$0.0879120\pi$
$810$	572.131	−	26.7627i	0.706334	−	0.0330404i
$811$		−	849.941i		−	1.04802i	−0.851713	−	0.524008i	$-0.824436\pi$
$811$		−	849.941i		−	1.04802i	0.851713	−	0.524008i	$-0.175564\pi$
$812$	241.296	+	318.048i	0.297163	+	0.391685i
$813$	−580.312	−	684.270i	−0.713790	−	0.841661i
$814$			224.867i			0.276249i
$815$	−1141.92	+	449.276i	−1.40113	+	0.551259i
$816$	341.066	+	28.0383i	0.417973	+	0.0343607i
$817$	1103.59	−	1103.59i	1.35078	−	1.35078i
$818$	392.358	−	392.358i	0.479656	−	0.479656i
$819$	−91.7931	+	296.309i	−0.112080	+	0.361793i
$820$	−151.600	+	348.267i	−0.184878	+	0.424715i
$821$			164.509i			0.200376i	0.994969	+	0.100188i	$0.0319445\pi$
$821$			164.509i			0.200376i	−0.994969	+	0.100188i	$0.968056\pi$
$822$	−550.871	−	649.555i	−0.670159	−	0.790213i
$823$	−90.7701	+	90.7701i	−0.110292	+	0.110292i	−0.760099	−	0.649807i	$-0.774850\pi$
$823$	−90.7701	+	90.7701i	−0.110292	+	0.110292i	0.649807	+	0.760099i	$0.274850\pi$
$824$		−	330.353i		−	0.400914i
$825$	−128.676	+	1087.77i	−0.155971	+	1.31850i
$826$	604.725	+	82.9790i	0.732113	+	0.100459i
$827$	−369.738	+	369.738i	−0.447083	+	0.447083i	−0.894384	−	0.447300i	$-0.852385\pi$
$827$	−369.738	+	369.738i	−0.447083	+	0.447083i	0.447300	+	0.894384i	$0.352385\pi$
$828$	39.7282	+	55.4902i	0.0479809	+	0.0670171i
$829$	−61.7867			−0.0745316			−0.0372658	−	0.999305i	$-0.511865\pi$
$829$	−61.7867			−0.0745316			−0.0372658	+	0.999305i	$0.511865\pi$
$830$	38.0211	−	87.3449i	0.0458085	−	0.105235i
$831$	1312.92	+	107.933i	1.57993	+	0.129883i
$832$	27.8534	−	27.8534i	0.0334776	−	0.0334776i
$833$	1217.73	−	685.419i	1.46187	−	0.822832i
$834$	14.4102	−	175.289i	0.0172784	−	0.210179i
$835$	84.4025	+	214.525i	0.101081	+	0.256916i
$836$	−771.513			−0.922863
$837$	−362.597	+	217.020i	−0.433210	+	0.259283i
$838$	−383.324	−	383.324i	−0.457427	−	0.457427i
$839$			77.9554i			0.0929146i	0.998920	+	0.0464573i	$0.0147931\pi$
$839$			77.9554i			0.0929146i	−0.998920	+	0.0464573i	$0.985207\pi$
$840$	−293.358	+	46.2734i	−0.349235	+	0.0550873i
$841$	−27.8443			−0.0331086
$842$	−809.373	+	809.373i	−0.961250	+	0.961250i
$843$	445.691	+	525.533i	0.528696	+	0.623408i
$844$		−	58.7279i		−	0.0695828i
$845$	288.877	−	663.631i	0.341867	−	0.785363i
$846$	61.9737	−	374.385i	0.0732550	−	0.442536i
$847$	−514.709	+	390.499i	−0.607685	+	0.461037i
$848$	−189.974	−	189.974i	−0.224026	−	0.224026i
$849$	−721.306	−	59.2971i	−0.849594	−	0.0698435i
$850$	−687.032	−	737.959i	−0.808273	−	0.868187i
$851$		−	41.2783i		−	0.0485056i
$852$	301.829	−	255.973i	0.354260	−	0.300438i
$853$	−1148.30	−	1148.30i	−1.34620	−	1.34620i	−0.889753	−	0.456443i	$-0.849123\pi$
$853$	−1148.30	−	1148.30i	−1.34620	−	1.34620i	−0.456443	−	0.889753i	$-0.650877\pi$
$854$	−531.353	−	72.9110i	−0.622193	−	0.0853759i
$855$	646.008	−	997.713i	0.755565	−	1.16692i
$856$	−502.217			−0.586702
$857$	−663.238	−	663.238i	−0.773906	−	0.773906i	0.204881	−	0.978787i	$-0.434319\pi$
$857$	−663.238	−	663.238i	−0.773906	−	0.773906i	−0.978787	+	0.204881i	$0.934319\pi$
$858$	197.332	+	232.683i	0.229991	+	0.271192i
$859$	726.339			0.845564			0.422782	−	0.906231i	$-0.361054\pi$
$859$	726.339			0.845564			0.422782	+	0.906231i	$0.361054\pi$
$860$	−216.335	−	549.856i	−0.251552	−	0.639367i
$861$	172.816	−	778.701i	0.200716	−	0.904414i
$862$	−432.674	−	432.674i	−0.501942	−	0.501942i
$863$	881.430	+	881.430i	1.02136	+	1.02136i	0.999767	+	0.0215890i	$0.00687252\pi$
$863$	881.430	+	881.430i	1.02136	+	1.02136i	0.0215890	+	0.999767i	$0.493127\pi$
$864$	148.134	+	37.2055i	0.171452	+	0.0430619i
$865$	−803.408	+	316.092i	−0.928796	+	0.365424i
$866$	576.898			0.666163
$867$	−1017.30	−	1199.54i	−1.17336	−	1.38355i
$868$	174.563	−	132.437i	0.201109	−	0.152577i
$869$	−624.059			−0.718134
$870$	−286.066	+	532.997i	−0.328812	+	0.612641i
$871$		−	480.388i		−	0.551536i
$872$	−3.21508	+	3.21508i	−0.00368702	+	0.00368702i
$873$	627.121	+	875.928i	0.718352	+	1.00335i
$874$	141.625			0.162042
$875$	730.632	+	481.459i	0.835008	+	0.550238i
$876$	−4.52640	+	55.0603i	−0.00516712	+	0.0628543i
$877$	1201.58	+	1201.58i	1.37010	+	1.37010i	0.860280	+	0.509822i	$0.170289\pi$
$877$	1201.58	+	1201.58i	1.37010	+	1.37010i	0.509822	+	0.860280i	$0.329711\pi$
$878$	652.665	−	652.665i	0.743354	−	0.743354i
$879$	64.8005	−	788.251i	0.0737207	−	0.896759i
$880$	−116.581	+	267.820i	−0.132479	+	0.304341i
$881$	403.967			0.458533			0.229266	−	0.973364i	$-0.426367\pi$
$881$	403.967			0.458533			0.229266	+	0.973364i	$0.426367\pi$
$882$	586.152	−	213.045i	0.664571	−	0.241548i
$883$	−740.709	+	740.709i	−0.838855	+	0.838855i	−0.988708	−	0.149853i	$-0.952120\pi$
$883$	−740.709	+	740.709i	−0.838855	+	0.838855i	0.149853	+	0.988708i	$0.452120\pi$
$884$	−280.836			−0.317687
$885$	266.965	+	885.516i	0.301656	+	1.00058i
$886$	−859.416			−0.969996
$887$	−703.405	−	703.405i	−0.793016	−	0.793016i	0.188968	−	0.981983i	$-0.439486\pi$
$887$	−703.405	−	703.405i	−0.793016	−	0.793016i	−0.981983	+	0.188968i	$0.939486\pi$
$888$	−59.7518	−	70.4559i	−0.0672880	−	0.0793422i
$889$	−387.563	−	53.1804i	−0.435954	−	0.0598205i
$890$	−50.1800	−	127.542i	−0.0563820	−	0.143306i
$891$	−381.203	+	1119.88i	−0.427837	+	1.25688i
$892$	−407.103	+	407.103i	−0.456394	+	0.456394i
$893$	−556.849	−	556.849i	−0.623571	−	0.623571i
$894$	65.8278	−	800.747i	0.0736329	−	0.895690i
$895$	−223.913	−	97.4688i	−0.250182	−	0.108904i
$896$	−78.4607	−	10.7662i	−0.0875678	−	0.0120158i
$897$	−36.2238	−	42.7131i	−0.0403833	−	0.0476177i
$898$	−544.342	+	544.342i	−0.606171	+	0.606171i
$899$		−	446.306i		−	0.496447i
$900$	−248.725	−	375.014i	−0.276361	−	0.416683i
$901$			1915.44i			2.12590i
$902$	−554.732	−	554.732i	−0.615002	−	0.615002i
$903$	666.476	+	1046.67i	0.738068	+	1.15911i
$904$		−	566.022i		−	0.626130i
$905$	−148.789	+	341.809i	−0.164407	+	0.377690i
$906$	−40.7840	+	496.107i	−0.0450154	+	0.547580i
$907$	−141.537	−	141.537i	−0.156050	−	0.156050i	0.624764	−	0.780814i	$-0.285195\pi$
$907$	−141.537	−	141.537i	−0.156050	−	0.156050i	−0.780814	+	0.624764i	$0.785195\pi$
$908$	−304.423	+	304.423i	−0.335267	+	0.335267i
$909$	165.881	−	1002.09i	0.182487	−	1.10241i
$910$	236.820	−	57.5703i	0.260242	−	0.0632640i
$911$		−	379.247i		−	0.416298i	−0.978097	−	0.208149i	$-0.933256\pi$
$911$		−	379.247i		−	0.416298i	0.978097	−	0.208149i	$-0.0667439\pi$
$912$	241.733	−	205.007i	0.265058	−	0.224789i
$913$	139.126	+	139.126i	0.152384	+	0.152384i
$914$	200.600			0.219475
$915$	−234.574	−	778.075i	−0.256365	−	0.850355i
$916$		−	438.890i		−	0.479138i
$917$	680.614	−	516.367i	0.742219	−	0.563105i
$918$	−559.227	−	934.357i	−0.609180	−	1.01782i
$919$			589.717i			0.641695i	0.947131	+	0.320847i	$0.103968\pi$
$919$			589.717i			0.641695i	−0.947131	+	0.320847i	$0.896032\pi$
$920$	21.4006	−	49.1631i	0.0232615	−	0.0534381i
$921$	3.39670	−	41.3184i	0.00368806	−	0.0448625i
$922$	−16.3102	+	16.3102i	−0.0176900	+	0.0176900i
$923$	−229.649	+	229.649i	−0.248807	+	0.248807i
$924$	132.897	−	598.827i	0.143828	−	0.648081i
$925$	−9.72109	+	272.007i	−0.0105093	+	0.294062i
$926$		−	802.938i		−	0.867104i
$927$	−854.705	+	611.927i	−0.922012	+	0.660115i
$928$	−114.064	+	114.064i	−0.122913	+	0.122913i
$929$			409.557i			0.440858i	0.975403	+	0.220429i	$0.0707457\pi$
$929$			409.557i			0.440858i	−0.975403	+	0.220429i	$0.929254\pi$
$930$	292.539	+	157.009i	0.314558	+	0.168827i
$931$	348.623	−	1246.41i	0.374461	−	1.33879i
$932$	−433.826	+	433.826i	−0.465478	+	0.465478i
$933$	−333.206	+	282.583i	−0.357134	+	0.302875i
$934$	742.962			0.795462
$935$	1937.89	−	762.441i	2.07261	−	0.815445i
$936$	−123.657	−	20.4696i	−0.132113	−	0.0218692i
$937$	−275.806	+	275.806i	−0.294350	+	0.294350i	−0.838796	−	0.544446i	$-0.816740\pi$
$937$	−275.806	+	275.806i	−0.294350	+	0.294350i	0.544446	+	0.838796i	$0.316740\pi$
$938$	−769.450	+	583.765i	−0.820310	+	0.622351i
$939$	−1497.25	−	123.086i	−1.59452	−	0.131082i
$940$	−277.446	+	109.158i	−0.295156	+	0.116126i
$941$	−769.189			−0.817416			−0.408708	−	0.912665i	$-0.634021\pi$
$941$	−769.189			−0.817416			−0.408708	+	0.912665i	$0.634021\pi$
$942$	479.291	+	565.153i	0.508802	+	0.599950i
$943$	101.831	+	101.831i	0.107986	+	0.107986i
$944$			246.635i			0.261266i
$945$	663.119	+	673.275i	0.701713	+	0.712460i
$946$	1220.42			1.29008
$947$	148.857	−	148.857i	0.157188	−	0.157188i	−0.624132	−	0.781319i	$-0.714547\pi$
$947$	148.857	−	148.857i	0.157188	−	0.157188i	0.781319	+	0.624132i	$0.214547\pi$
$948$	195.532	−	165.826i	0.206257	−	0.174921i
$949$		−	45.3370i		−	0.0477735i
$950$	−933.253	−	33.3529i	−0.982371	−	0.0351083i
$951$	47.4435	−	577.115i	0.0498880	−	0.606851i
$952$	341.270	+	449.822i	0.358477	+	0.472502i
$953$	−99.9670	−	99.9670i	−0.104897	−	0.104897i	0.652710	−	0.757608i	$-0.273632\pi$
$953$	−99.9670	−	99.9670i	−0.104897	−	0.104897i	−0.757608	+	0.652710i	$0.773632\pi$
$954$	−139.613	+	843.404i	−0.146345	+	0.884071i
$955$	43.9048	−	100.862i	0.0459736	−	0.105614i
$956$			523.788i			0.547896i
$957$	−808.103	−	952.869i	−0.844413	−	0.995683i
$958$	615.307	+	615.307i	0.642283	+	0.642283i
$959$	191.031	−	1392.18i	0.199198	−	1.45170i
$960$	−34.6377	−	114.892i	−0.0360809	−	0.119679i
$961$	716.042			0.745101
$962$	53.6069	+	53.6069i	0.0557244	+	0.0557244i
$963$	930.276	+	1299.36i	0.966019	+	1.34928i
$964$	375.938			0.389978
$965$	−485.388	+	190.970i	−0.502992	+	0.197897i
$966$	−24.3956	+	109.925i	−0.0252543	+	0.113794i
$967$	−452.536	−	452.536i	−0.467979	−	0.467979i	0.433280	−	0.901259i	$-0.357356\pi$
$967$	−452.536	−	452.536i	−0.467979	−	0.467979i	−0.901259	+	0.433280i	$0.857356\pi$
$968$	−184.593	−	184.593i	−0.190695	−	0.190695i
$969$	−2252.16	−	185.146i	−2.32421	−	0.191069i
$970$	337.814	−	776.053i	0.348262	−	0.800055i
$971$	−625.077			−0.643746			−0.321873	−	0.946783i	$-0.604312\pi$
$971$	−625.077			−0.643746			−0.321873	+	0.946783i	$0.604312\pi$
$972$	−178.135	−	452.177i	−0.183267	−	0.465202i
$973$	231.183	−	175.394i	0.237599	−	0.180261i
$974$	−1194.20			−1.22608
$975$	228.642	+	289.993i	0.234504	+	0.297429i
$976$		−	216.711i		−	0.222040i
$977$	172.179	−	172.179i	0.176232	−	0.176232i	−0.613479	−	0.789711i	$-0.710230\pi$
$977$	172.179	−	172.179i	0.176232	−	0.176232i	0.789711	+	0.613479i	$0.210230\pi$
$978$	673.474	+	794.122i	0.688624	+	0.811986i
$979$	283.082			0.289154
$980$	−379.994	−	309.361i	−0.387749	−	0.315675i
$981$	14.2736	+	2.36278i	0.0145501	+	0.00240855i
$982$	−11.7151	−	11.7151i	−0.0119298	−	0.0119298i
$983$	612.197	−	612.197i	0.622785	−	0.622785i	−0.323458	−	0.946243i	$-0.604845\pi$
$983$	612.197	−	612.197i	0.622785	−	0.622785i	0.946243	+	0.323458i	$0.104845\pi$
$984$	321.214	+	26.4064i	0.326437	+	0.0268358i
$985$	−819.091	+	322.262i	−0.831565	+	0.327170i
$986$	1150.06			1.16639
$987$	528.131	−	336.291i	0.535087	−	0.340720i
$988$	−183.924	+	183.924i	−0.186158	+	0.186158i
$989$	−224.029			−0.226521
$990$	908.864	−	194.469i	0.918044	−	0.196433i
$991$	1736.43			1.75220			0.876102	−	0.482125i	$-0.160135\pi$
$991$	1736.43			1.75220			0.876102	+	0.482125i	$0.160135\pi$
$992$	62.6045	+	62.6045i	0.0631094	+	0.0631094i
$993$	−727.455	+	616.936i	−0.732583	+	0.621285i
$994$	646.903	+	88.7665i	0.650808	+	0.0893024i
$995$	−1486.23	−	646.955i	−1.49370	−	0.650206i
$996$	−80.5602	−	6.62270i	−0.0808838	−	0.00664929i
$997$	−817.471	+	817.471i	−0.819930	+	0.819930i	−0.986098	−	0.166167i	$-0.946861\pi$
$997$	−817.471	+	817.471i	−0.819930	+	0.819930i	0.166167	+	0.986098i	$0.446861\pi$
$998$	11.1783	+	11.1783i	0.0112007	+	0.0112007i
$999$	−71.6061	+	285.101i	−0.0716778	+	0.285386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.k.a.167.4	yes	32
3.2	odd	2		210.3.k.b.167.12	yes	32
5.3	odd	4		210.3.k.b.83.5	yes	32
7.6	odd	2	inner	210.3.k.a.167.13	yes	32
15.8	even	4	inner	210.3.k.a.83.13	yes	32
21.20	even	2		210.3.k.b.167.5	yes	32
35.13	even	4		210.3.k.b.83.12	yes	32
105.83	odd	4	inner	210.3.k.a.83.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.k.a.83.4	✓	32	105.83	odd	4	inner
210.3.k.a.83.13	yes	32	15.8	even	4	inner
210.3.k.a.167.4	yes	32	1.1	even	1	trivial
210.3.k.a.167.13	yes	32	7.6	odd	2	inner
210.3.k.b.83.5	yes	32	5.3	odd	4
210.3.k.b.83.12	yes	32	35.13	even	4
210.3.k.b.167.5	yes	32	21.20	even	2
210.3.k.b.167.12	yes	32	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-2.28799 + 1.94039i) q^{3} -2.00000i q^{4} +(4.58449 + 1.99562i) q^{5} +(0.347606 - 4.22838i) q^{6} +(5.57668 - 4.23091i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.46981 - 8.87917i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-2.28799 + 1.94039i) q^{3} -2.00000i q^{4} +(4.58449 + 1.99562i) q^{5} +(0.347606 - 4.22838i) q^{6} +(5.57668 - 4.23091i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.46981 - 8.87917i) q^{9} +(-6.58010 + 2.58887i) q^{10} -14.6047i q^{11} +(3.88077 + 4.57598i) q^{12} +(-3.48167 - 3.48167i) q^{13} +(-1.34578 + 9.80759i) q^{14} +(-14.3615 + 4.32971i) q^{15} -4.00000 q^{16} +(20.1653 + 20.1653i) q^{17} +(7.40936 + 10.3490i) q^{18} +26.4132 q^{19} +(3.99123 - 9.16897i) q^{20} +(-4.54981 + 20.5012i) q^{21} +(14.6047 + 14.6047i) q^{22} +(-2.68095 - 2.68095i) q^{23} +(-8.45675 - 0.695213i) q^{24} +(17.0350 + 18.2978i) q^{25} +6.96334 q^{26} +(13.8661 + 23.1675i) q^{27} +(-8.46182 - 11.1534i) q^{28} -28.5159 q^{29} +(10.0318 - 18.6912i) q^{30} +15.6511i q^{31} +(4.00000 - 4.00000i) q^{32} +(28.3387 + 33.4154i) q^{33} -40.3306 q^{34} +(34.0095 - 8.26762i) q^{35} +(-17.7583 - 2.93962i) q^{36} +(7.69844 + 7.69844i) q^{37} +(-26.4132 + 26.4132i) q^{38} +(14.7218 + 1.21025i) q^{39} +(5.17774 + 13.1602i) q^{40} -37.9832 q^{41} +(-15.9514 - 25.0510i) q^{42} +(41.7817 - 41.7817i) q^{43} -29.2094 q^{44} +(24.4578 - 37.7732i) q^{45} +5.36190 q^{46} +(-21.0822 - 21.0822i) q^{47} +(9.15197 - 7.76154i) q^{48} +(13.1988 - 47.1889i) q^{49} +(-35.3328 - 1.26273i) q^{50} +(-85.2664 - 7.00958i) q^{51} +(-6.96334 + 6.96334i) q^{52} +(47.4934 + 47.4934i) q^{53} +(-37.0336 - 9.30137i) q^{54} +(29.1453 - 66.9549i) q^{55} +(19.6152 + 2.69155i) q^{56} +(-60.4332 + 51.2518i) q^{57} +(28.5159 - 28.5159i) q^{58} -61.6589i q^{59} +(8.65943 + 28.7231i) q^{60} +54.1777i q^{61} +(-15.6511 - 15.6511i) q^{62} +(-29.3703 - 55.7350i) q^{63} +8.00000i q^{64} +(-9.01359 - 22.9098i) q^{65} +(-61.7541 - 5.07668i) q^{66} +(68.9882 + 68.9882i) q^{67} +(40.3306 - 40.3306i) q^{68} +(11.3361 + 0.931915i) q^{69} +(-25.7419 + 42.2771i) q^{70} -65.9594i q^{71} +(20.6980 - 14.8187i) q^{72} +(6.51081 + 6.51081i) q^{73} -15.3969 q^{74} +(-74.4807 - 8.81061i) q^{75} -52.8265i q^{76} +(-61.7911 - 81.4457i) q^{77} +(-15.9321 + 13.5116i) q^{78} -42.7301i q^{79} +(-18.3379 - 7.98247i) q^{80} +(-76.6793 - 26.1014i) q^{81} +(37.9832 - 37.9832i) q^{82} +(-9.52614 + 9.52614i) q^{83} +(41.0024 + 9.09963i) q^{84} +(52.2053 + 132.690i) q^{85} +83.5634i q^{86} +(65.2441 - 55.3318i) q^{87} +(29.2094 - 29.2094i) q^{88} +19.3830i q^{89} +(13.3155 + 62.2310i) q^{90} +(-34.1468 - 4.68555i) q^{91} +(-5.36190 + 5.36190i) q^{92} +(-30.3692 - 35.8096i) q^{93} +42.1644 q^{94} +(121.091 + 52.7107i) q^{95} +(-1.39043 + 16.9135i) q^{96} +(-84.6391 + 84.6391i) q^{97} +(33.9901 + 60.3877i) q^{98} +(-129.677 - 21.4661i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} - 4 q^{7} + 64 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q - 32 * q^2 - 4 * q^7 + 64 * q^8 - 16 * q^9	\( 32 q - 32 q^{2} - 4 q^{7} + 64 q^{8} - 16 q^{9} + 8 q^{14} - 20 q^{15} - 128 q^{16} + 36 q^{18} + 12 q^{21} - 40 q^{22} + 24 q^{23} + 16 q^{25} - 8 q^{28} - 112 q^{29} + 68 q^{30} + 128 q^{32} - 48 q^{35} - 40 q^{36} + 32 q^{37} + 64 q^{39} - 44 q^{42} - 32 q^{43} + 80 q^{44} - 48 q^{46} - 8 q^{50} + 84 q^{51} - 136 q^{53} + 244 q^{57} + 112 q^{58} - 96 q^{60} + 72 q^{63} - 200 q^{65} + 32 q^{67} + 8 q^{72} - 64 q^{74} + 88 q^{77} - 124 q^{78} + 76 q^{81} + 64 q^{84} - 40 q^{85} - 80 q^{88} - 272 q^{91} + 48 q^{92} - 452 q^{93} + 544 q^{95} + 128 q^{98} + 160 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 4 * q^7 + 64 * q^8 - 16 * q^9 + 8 * q^14 - 20 * q^15 - 128 * q^16 + 36 * q^18 + 12 * q^21 - 40 * q^22 + 24 * q^23 + 16 * q^25 - 8 * q^28 - 112 * q^29 + 68 * q^30 + 128 * q^32 - 48 * q^35 - 40 * q^36 + 32 * q^37 + 64 * q^39 - 44 * q^42 - 32 * q^43 + 80 * q^44 - 48 * q^46 - 8 * q^50 + 84 * q^51 - 136 * q^53 + 244 * q^57 + 112 * q^58 - 96 * q^60 + 72 * q^63 - 200 * q^65 + 32 * q^67 + 8 * q^72 - 64 * q^74 + 88 * q^77 - 124 * q^78 + 76 * q^81 + 64 * q^84 - 40 * q^85 - 80 * q^88 - 272 * q^91 + 48 * q^92 - 452 * q^93 + 544 * q^95 + 128 * q^98 + 160 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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